<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>

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Orthogonal Functions, Orthogonal Polynomials, and Orthogonal Wavelets series expansions of function

\302\251 Sergey Moiseev 2009

Kodofon

Russia

smoiseev@kodofon.vrn.ru, snmoiseev@yandex.ru

As you read this worksheet, you should execute the commands in sequence as you come to them.

<Text-field style="Heading 1" layout="Heading 1">Introduction</Text-field>

The worksheet includes all the best known continuous orthogonal series expansions in the closed form. It demonstrates the use of Maple to evaluate expansion of a function by Fourier, Hartley, Fourier-Bessel, Orthogonal Rational Tangent, Rectangular, Haar Wavelet, Walsh, Slant, Piece-Linear-Quadratic, Associated Legandre, Orthogonal Rational, Generalized sinc, Sinc, Sinc Wavelet, Jacobi, Chebyshev first kind, Chebyshev second kind, Gegenbauer, Generalized Laguerre, Laguerre, Hermite, and classical polynomials orthogonal series. Also the worksheet demonstrates how to create new orthonormal basis of functions by using the Gram-Schmidt orthogonalization process by the example of Slant, and Piece-Linear-Quadratic orthonormal functions creating.

<Text-field style="Heading 1" layout="Heading 1">Initialization of expansion procedures</Text-field>

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUShyZXN0YXJ0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjhRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiO0YnRj0vJSZmZW5jZUdGPC8lKnNlcGFyYXRvckdGNi8lKXN0cmV0Y2h5R0Y8LyUqc3ltbWV0cmljR0Y8LyUobGFyZ2VvcEdGPC8lLm1vdmFibGVsaW1pdHNHRjwvJSdhY2NlbnRHRjwvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR1EsMC4yNzc3Nzc4ZW1GJ0Y6Rj0=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2JVEld2l0aEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRJnBsb3RzRidGL0YyLyUrZXhlY3V0YWJsZUdRJmZhbHNlRicvRjNRJ25vcm1hbEYnRkAtSSNtb0dGJDYtUSI6RidGQC8lJmZlbmNlR0Y/LyUqc2VwYXJhdG9yR0Y/LyUpc3RyZXRjaHlHRj8vJSpzeW1tZXRyaWNHRj8vJShsYXJnZW9wR0Y/LyUubW92YWJsZWxpbWl0c0dGPy8lJ2FjY2VudEdGPy8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlZGPUZA

Gram-Schmidt orthogonalization for L2 space

The GramSchmidL2(f, x = a..b) calling sequence computes a list of orthonormal functions on the interval from a to b by using the Gram-Schmidt orthogonalization process.

f - the list of algebraic expressions representing the initial linear independant set of functions LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYxLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnL0YwUSdpdGFsaWNGJy1GIzYlLUZKNiVRImlGJ0ZNRlBGTUZQLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictRiw2LVEqJkVsZW1lbnQ7RidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjI3Nzc3NzhlbUYnL0ZFRmhuLUklbXN1cEdGJDYlLUZKNiVRIkxGJ0ZNRlAtRiM2JS1JI21uR0YkNiRRIjJGJ0YvRk1GUC8lMXN1cGVyc2NyaXB0c2hpZnRHRlktSShtZmVuY2VkR0YkNiQtRiM2Jy1GSjYlUSJhRidGTUZQLUYsNi1RIixGJ0YvRjIvRjZGT0Y3RjlGO0Y9Rj9GQS9GRVEsMC4zMzMzMzMzZW1GJy1GSjYlUSJiRidGTUZQLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0YvRi9GYHBGK0ZULUYsNi1RIj1GJ0YvRjJGNUY3RjlGO0Y9Rj9GZ25GaW4tRmNvNiRRIjFGJ0YvLUYsNi1RIy4uRidGL0YyRjVGN0Y5RjtGPUY/L0ZCUSwwLjIyMjIyMjJlbUYnRkQtRko2JVElbm9wc0YnRk1GUC1GaW82JC1GIzYlRklGaXBGL0YvRmlwRi8=. x - the variable name appearing in LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVEiZkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYlLUYvNiVRImlGJ0YyRjVGMkY1LyUvc3Vic2NyaXB0c2hpZnRHUSIwRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnL0Y2USdub3JtYWxGJw==.

a, b - endpoints of interval of the orthogonalization.

It returns list of LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JVElbm9wc0YnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JKG1mZW5jZWRHRiQ2JC1GIzYlLUYsNiVRImZGJ0YvRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnL0YzUSdub3JtYWxGJ0ZARj1GQA== orthonormal functions (algebraic expressions).

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

Fourier expansion of a function

The FourierE(f, x = a..b, n) calling sequence computes the Fourier series expansion

of the expression f with respect to the variable x on the interval from a to b as folows:

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

fLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEqJkVsZW1lbnQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkMtSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJMRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRidGL0ZNRlAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkobWZlbmNlZEdGJDYmLUYjNictRko2JVEiYUYnRk1GUC1GLDYtUSIsRidGL0YyL0Y2Rk9GN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFUSwwLjMzMzMzMzNlbUYnLUZKNiVRImJGJ0ZNRlAvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRi9GLy8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJy1GSjYjUSFGJ0Zob0Yv - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients 2n+1.

It returns list of n Fourier expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Cas (cosin and sine) functions

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

Hartley expansion of a function

The HartleyE(f, x = a..b, n) calling sequence computes the Hartley series expansion

of the expression f with respect to the variable x on the interval from a to b as folows:

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients 2n+1.

It returns list of n Hartley expansions of function f(x) for terms of expansion n=1,2,..,n.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZqdi1JI21pR0YkNiVRKUhhcnRsZXlFRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjY2L1ElcHJvY0YnLyUlYm9sZEdGMS9GM1ElYm9sZEYnLyUrZm9udHdlaWdodEdGVUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlktSShtZmVuY2VkR0YkNiQtRiM2KC1GLDYlUSJmRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGWC9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSNhYkYnRi9GMkZdby1GLDYlUSJuRidGL0YyRjlGOS1GLDYjUSFGJy1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZhcC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GNjYvUSZsb2NhbEYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGWEZaLUYsNiVRImFGJ0YvRjJGXW8tRiw2JVEiYkYnRi9GMkZdby1GLDYlUSJpRidGL0YyRl1vLUYsNiVRImRGJ0YvRjJGXW8tRiw2JVEic0YnRi9GMkZdby1GLDYlUSJMRidGL0YyRl1vLUYsNiVRInhGJ0YvRjItRjY2LVEiO0YnRjlGO0Zgb0ZARkJGREZGRkhGWEZNRl1xRl9yRjUtRmZuNiYtRiM2JEZpb0Y5RjkvJSVvcGVuR1EiW0YnLyUmY2xvc2VHUSJdRidGZXJGXHBGYnJGNS1GLDYlUSRsaHNGJ0YvRjItRmZuNiQtRiM2JUZjby8lK2V4ZWN1dGFibGVHRj1GOUY5RmVyRmBxRjVGYnMtRmZuNiQtRiM2JS1GLDYlUSRyaHNGJ0YvRjItRmZuNiQtRiM2JEZjb0Y5RjlGOUY5RmVyRmNxRjVGX3RGW3RGZXJGaXFGNUZjcS1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmp0RmBxRmVyRl1xRlxyRjUtSSNtbkdGJDYkUSIwRidGOUZlckZdcUZdcUZccEZdcS1GNjYvUSRmb3JGJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZdcUZmcUZdcUZdcS1GNjYvUSVmcm9tRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGXXFGXHVGXXEtRjY2L1EjdG9GJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZdcUZdcUZmb0ZdcUZdcS1GNjYvUSNkb0YnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRl1xRlxwRl1xRl1xRl1xRl1xRl1xRl1xRl1xRlxyRjVGXHItRjY2LVEiK0YnRjlGO0Y+RkBGQkZERkZGSEZpdEZbdS1JJm1mcmFjR0YkNigtRiM2JC1GXXU2JFEiMUYnRjlGOS1GIzYkRmlxRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl53LyUpYmV2ZWxsZWRHRj1GXXEtRiw2JVEmZXZhbGZGJ0YvRjItRmZuNiQtRiM2Ky1JKG1zdWJzdXBHRiQ2Jy1JJ21zdHlsZUdGJDYmLUY2NjBRJiZpbnQ7RicvJStmb3JlZ3JvdW5kR1EuWzE0NCwxNDQsMTQ0XUYnRmlzRjkvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnRjtGPi9GQUYxRkIvRkVGMUZGRkhGWEZaRmN4RmlzRjktRiw2J0ZicUYvL0ZkeFEsWzEyOCwwLDEyOF1GJy8lLHBsYWNlaG9sZGVyR0YxRjItRiw2J0ZlcUYvRl15Rl95RjIvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLyUvc3Vic2NyaXB0c2hpZnRHRmV5RmpuRl1xLUYsNiVRJENhc0YnRi9GMi1GZm42JC1GIzYoRmZxRl1vLUZgdjYoLUYjNiRGYnJGOUZndkZpdkZcd0Zfd0Zhd0ZcdkZgcUY5RjlGXXEtRl54NiYtRjY2MFEwJkRpZmZlcmVudGlhbEQ7RidGY3hGaXNGOUZmeEY7Rj5GQEZCRkRGRkZIRlhGWkZjeEZpc0Y5LUYsNidGZHJGL0ZdeUZfeUYyRjlGOUZdcUZoeUZbekZlckZccEZdcUZdcUZdcUZdcUZdcUZdcUZdcS1GNjYvUSNpZkYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRl1xRmZxLUY2Ni1RIj5GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRlx1Rl1xLUY2Ni9RJXRoZW5GJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZdcUZccEZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZdcUZcckY1RlxyRlx2Rl92Rl1xRmN3LUZmbjYkLUYjNitGandGam5GXXFGaHktRmZuNiQtRiM2KS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGaXRGW3VGZnFGXW9GX3pGXHZGYHFGOUY5Rl1xRmN6Rmh6RjlGOUZdcUZoeUZnW2xGaW9GXHBGXXFGXXFGXXFGXXFGXXFGXXFGXXEtRjY2L1EkZW5kRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGXXFGanpGZXJGXHBGXXFGXXFGXXFGXXFGXXFGXXFGXXFGanpGXXFGZnFGXVtsRlx1Rl1xRmBbbEZdcUZfckY1LUZmbjYmLUYjNigtRiw2JVEjb3BGJ0YvRjItRmZuNiQtRiM2JEZfckY5RjlGXW8tRiM2JUZjdy1GZm42JC1GIzYkRlxyRjlGOUY5RmlvRjlGOUZcc0Zfc0ZlckZdcUZeXGxGXXFGanpGZXJGXHBGXXFGXlxsRl1xRml1LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNRlxwRl1xRl5cbEZdcUZPRmJdbEZpc0Y5

Fourier-Bessel expansion of a function

The FourierBesselE(f, x = a..b, n, v) calling sequence computes the Fourier-Bessel series expansion of the expression f with respect to the variable x on the interval from a to b

as folows:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY6LUkjbWlHRiQ2JlEiZkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1Ri8vJSlyZWFkb25seUdGNC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnL0Y2USdub3JtYWxGJ0YvRkUtSSNtb0dGJDYuUSkmYXBwcm94O0YnRi9GRS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTS8lKXN0cmV0Y2h5R0ZNLyUqc3ltbWV0cmljR0ZNLyUobGFyZ2VvcEdGTS8lLm1vdmFibGVsaW1pdHNHRk0vJSdhY2NlbnRHRk0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zmbi1JK211bmRlcm92ZXJHRiQ2Jy1JJ21zdHlsZUdGJDYmLUZINi9RJiZzdW07RicvJSdvcGFxdWVHRjRGRS9JK21zZW1hbnRpY3NHRiRRJmluZXJ0RidGS0ZOL0ZRRjRGUi9GVUY0L0ZXRjRGWC9GZW5RJjAuMGVtRicvRmhuUSwwLjE2NjY2NjdlbUYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Zib0ZFLUYjNigtRiw2JVEiaUYnRjJGNS1GSDYtUSkmZXF1YWxzO0YnRkVGS0ZORlBGUkZURlZGWEZaRmduLUkjbW5HRiQ2JFEiMUYnRkVGQEZCRkUtRiw2JVEibkYnRjJGNS8lJ2FjY2VudEdGTS8lLGFjY2VudHVuZGVyR0ZNLUkmbWZyYWNHRiQ2KC1GIzYlLUklbXN1YkdGJDYlLUYsNiZRIkpGJ0YyRjUvRmVvUShCZXNzZWxKRictRiw2JVEidkYnRjJGNS8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnLUY5NiQtRmVxNigtRiM2Ji1GanE2JS1GLDYlUSUmbXU7RicvRjNGTUZFRmNwRmRyLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGTkZQRlJGVEZWRlhGam8vRmhuRltwLUY5NiQtRiM2Ji1GLDYlRj9GMkY1LUZINi1RKCZtaW51cztGJ0ZFRktGTkZQRlJGVEZWRlgvRmVuUSwwLjIyMjIyMjJlbUYnL0ZobkZhdC1GLDYlUSJhRidGMkY1RkVGRUZFLUYjNiYtRiw2JVEiYkYnRjJGNUZddEZjdEZFLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZgdS8lKWJldmVsbGVkR0ZNRkVGRS1GIzYnLUYsNiNRIUYnLUYjNiYtSSVtc3VwR0YkNiUtRjk2JEZmdEZFLUYjNiQtRmpwNiRRIjJGJ0ZFRkUvJTFzdXBlcnNjcmlwdHNoaWZ0R0ZmckZjcy1GXXY2JS1GIzYmLUZqcTYlRlxyLUYjNiZGYXItRkg2LVEnJnBsdXM7RidGRUZLRk5GUEZSRlRGVkZYRmB0RmJ0RmlwRkVGZHItRkg2LVEwJkFwcGx5RnVuY3Rpb247RidGRUZLRk5GUEZSRlRGVkZYRmpvRmZzLUY5NiRGXXNGRUZFRmN2RmZ2RkVGZ3VGMkY1Rlt1Rl51RmF1RmN1LUZINi1RIn5GJ0ZFRktGTkZQRlJGVEZWRlhGam9GZnMtSShtc3Vic3VwR0YkNictRl1vNiYtRkg2L1EmJmludDtGJ0Zib0ZFRmRvRktGTkZnb0ZSRmhvRlZGWEZqb0Zmc0ZecEZib0ZFRmN0Rmh0RmZ2RmRyLUYsNiVGLkYyRjUtRjk2JEZbdEZFRmNzRmdzRmNzRmlxRmdyLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjNlbUYnLyUmZGVwdGhHRlx5LyUqbGluZWJyZWFrR1ElYXV0b0YnLUZdbzYmLUZINi9RMCZEaWZmZXJlbnRpYWxEO0YnRmJvRkVGZG9GS0ZORlBGUkZURlZGWEZqb0Zmc0ZecEZib0ZFRlt0LUZINi1RIixGJ0ZFRksvRk9GNEZQRlJGVEZWRlhGam8vRmhuUSwwLjMzMzMzMzNlbUYnLUZoeDYmRmp4L0ZeeVEmMC4wZW1GJ0ZgeS9GY3lRKG5ld2xpbmVGJ0ZndUYvRkBGQkZFwhere LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUklbXN1YkdGJDYlLUkjbWlHRiQ2JVElJm11O0YnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRictRi82JVEiaUYnL0YzUSV0cnVlRicvRjZRJ2l0YWxpY0YnLyUvc3Vic2NyaXB0c2hpZnRHUSIwRictSSNtb0dGJDYtUSJ+RidGNS8lJmZlbmNlR0Y0LyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRlZGNQ==is increasing positive zeroes of the BesselJ(v,x) function. 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 - the algebraic expression representing the function.

x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

v>-1/2 - the order of BesselJ function.

It returns list of n Fourier-Bessel expansions of function f(x) for terms of expansion

n=1,2,..,n.

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

Orthogonal Rational Tangent functions

The Rattan(p, j, x) calling sequence computes the j-th Orthogonal Rational Tangent function.

p\342\210\210\342\204\235, p\342\211\2400 - the form factor.

jLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2L1EqJkVsZW1lbnQ7RicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkgtSSNtaUdGJDYlUSsmaW50ZWdlcnM7RicvJSdpdGFsaWNHRjkvRjNRJ25vcm1hbEYnRlE= - the function number.

x - the argument of the function.

This functions are orthonormal on the interval LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNigtSSNtb0dGJDYtUSomdW1pbnVzMDtGJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRjkvJSlzdHJldGNoeUdGOS8lKnN5bW1ldHJpY0dGOS8lKGxhcmdlb3BHRjkvJS5tb3ZhYmxlbGltaXRzR0Y5LyUnYWNjZW50R0Y5LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGSC1JJm1mcmFjR0YkNigtSSNtaUdGJDYlUScmIzk2MDtGJy8lJ2l0YWxpY0dGOUY0LUYjNiUtSSNtbkdGJDYkUSIyRidGNC9GU1EldHJ1ZUYnL0Y1USdpdGFsaWNGJy8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGXW8vJSliZXZlbGxlZEdGOS1GMTYtUSIsRidGNEY3L0Y7RmVuRjxGPkZARkJGRC9GR1EmMC4wZW1GJy9GSlEsMC4zMzMzMzMzZW1GJ0ZLLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Y0RjRGam9GNA==.

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

Orthogonal Rational Tangent expansion of a function

The RattanE(f, x=a..b, n, p) calling sequence computes the Orthogonal Rational Tangent series expansion of the expression f with respect to the variable x on the interval from a to b as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients 2n.

p\342\210\210\342\204\235, p\342\211\2400 - the form factor.

It returns list of n Orthogonal Rational Tangent expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Associated Legendre functions expansion of a function

The LegendreE(f, x = a..b, n, m) calling sequence computes the Associated Legendre series expansion of the expression f with respect to the variable x on the interval from a to b as folows:

where 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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

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parameters (order) of the Associated Legandre function.

It returns list of n Associated Legandre expansions of function f(x) for terms of expansion

n=1,2,..,n.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2I1EhRic=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2J1EibUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRictSSNtb0dGJDYtUSI9RicvRjVRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZCLyUpc3RyZXRjaHlHRkIvJSpzeW1tZXRyaWNHRkIvJShsYXJnZW9wR0ZCLyUubW92YWJsZWxpbWl0c0dGQi8lJ2FjY2VudEdGQi8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRlEtSSNtbkdGJDYkUSIwRidGPkY+ then the procedure returns Legendre polynomials expansion.

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

Jacobi polynomials expansion of a function

The JacobiE(f, x = a..b, n, 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) calling sequence computes the Jacobi polynomials series expansion of the expression f with respect to the variable x on the interval from a to b

as folows:

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

where 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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYwLUkjbWlHRiQ2J1EnJiM5NDU7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNy1JI21vR0YkNi1RIj5GJy9GNlEnbm9ybWFsRicvJSZmZW5jZUdGNC8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZQLUY7Ni1RKiZ1bWludXMwO0YnRj5GQEZCRkRGRkZIRkpGTC9GT1EsMC4yMjIyMjIyZW1GJy9GUkZXLUkjbW5HRiQ2JFEiMUYnRj4tRjs2LVEiLEYnRj5GQC9GQ0YxRkRGRkZIRkpGTC9GT1EmMC4wZW1GJy9GUlEsMC4zMzMzMzMzZW1GJy1GOzYtUSJ+RidGPkZARkJGREZGRkhGSkZMRltvL0ZSRlxvLUYsNidRJyYjOTQ2O0YnRi9GMkY1RjhGOkZTRllGX29GU0Zfb0Y+parameters of the Jacobi polynomial.

It returns list of n Jacobi polynomials expansions of function f(x) for terms of expansion

n=1,2,..,n.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 then the procedure returns Legendre polynomials expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 then the procedure returns Chebyshev first kind polynomials expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 then the procedure returns Chebyshev second kind polynomials expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 the procedure returns Gegenbauer polynomials expansion.

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

Jacobi functions expansion of a function

The JacobiFE(f, x = a..b, n, 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) calling sequence computes the Jacobi functions series expansion of the expression f with respect to the variable x on the interval from a to b

as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

It returns list of n Jacobi functions expansions of function f(x) for terms of expansion

n=1,2,..,n.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 then the procedure returns Chebyshev first kind functions expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 then the procedure returns Chebyshev second kind functions expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2J1EoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjQ=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 the procedure returns Gegenbauer functions expansion.

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

Rect function

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

Rect expansion of a function

The RectE(f, x = a..b, n) calling sequence computes the Rect series expansion

of the expression f with respect to the variable x on the interval from a to b as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

It returns list of n Rect expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Haar functions (Haar wavelets)

The Haar(n, j, x) calling sequence computes the j-th Haar function (wavelet)

of order n (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) on interval [0,1).

n - the order of the Haar function (scale of the wavelet) 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.

j - the Haar function number (shift of the wavelet) (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).

x - the argument of Haar function.

This functions are orthonormal on the interval LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYlLUYjNictSSNtbkdGJDYkUSIwRicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLUkjbW9HRiQ2LVEiLEYnRjQvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHUSV0cnVlRicvJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EmMC4wZW1GJy8lJ3JzcGFjZUdRLDAuMzMzMzMzM2VtRictRjE2JFEiMUYnRjQvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjRGNC8lJW9wZW5HUSJbRidGVEY0.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVElSGFhckYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKSZBc3NpZ247RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiQtRiM2KS1GLDYlUSJuRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEiakYnRi9GMkZXLUYsNiVRInhGJ0YvRjIvJStleGVjdXRhYmxlR0Y9RjlGOS1GNjYtUSYmbWFwO0YnRjlGO0Y+L0ZBRjFGQkZERkZGSEZKRk0tRlA2KC1JJ210YWJsZUdGJDY3LUkkbXRyR0YkNictSSRtdGRHRiQ2KC1JJm1zcXJ0R0YkNiMtSSVtc3VwR0YkNiUtSSNtbkdGJDYkUSIyRidGOUZULyUxc3VwZXJzY3JpcHRzaGlmdEdRIjBGJy8lKXJvd2FsaWduR1EhRicvJSxjb2x1bW5hbGlnbkdGX3EvJStncm91cGFsaWduR0ZfcS8lKHJvd3NwYW5HUSIxRicvJStjb2x1bW5zcGFuR0ZmcS1GXnA2KC1GIzYoLUkmbWZyYWNHRiQ2KC1GIzYmRmZwLUY2Ni1RMSZJbnZpc2libGVUaW1lcztGJ0Y5RjtGPkZARkJGREZGRkhGZW4vRk5GZm5GaW5GOS1GZHA2JUZmcC1GIzYmRlQtRjY2LVEnJnBsdXM7RidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORl5zLUZncDYkUSIxRidGOUY5RmpwLyUubGluZXRoaWNrbmVzc0dGZnEvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGZ3MvJSliZXZlbGxlZEdGPS1GNjYtUSUmbGU7RidGOUY7Rj5GQEZCRkRGRkZIRkpGTUZcby1GNjYtUSUmbHQ7RidGOUY7Rj5GQEZCRkRGRkZIRkpGTS1GXnI2KC1GIzYnLUYsNiNGX3FGYHJGanJGYHNGOUZmckZjc0Zlc0Zoc0Zqc0Y5Rl1xRmBxRmJxRmRxRmdxRl1xRmBxRmJxLUZbcDYnLUZecDYoLUYjNiUtRjY2LVEqJnVtaW51czA7RidGOUY7Rj5GQEZCRkRGRkZIRl1zRl9zRmBwRjlGXXFGYHFGYnFGZHFGZ3EtRl5wNigtRiM2KEZidEZcdEZcb0ZfdC1GXnI2KC1GIzYnRmZ0RmByRmpyRmZwRjlGZnJGY3NGZXNGaHNGanNGOUZdcUZgcUZicUZkcUZncUZdcUZgcUZicS1GW3A2Jy1GXnA2KC1GZ3A2JFEiMEYnRjlGXXFGYHFGYnFGZHFGZ3EtRl5wNigtRiw2JVEqb3RoZXJ3aXNlRidGL0YyRl1xRmBxRmJxRmRxRmdxRl1xRmBxRmJxLyUmYWxpZ25HUSVheGlzRicvRl5xUSliYXNlbGluZUYnL0ZhcUZncy9GY3FRJ3xmcmxlZnR8aHJGJy8lL2FsaWdubWVudHNjb3BlR0YxLyUsY29sdW1ud2lkdGhHUSVhdXRvRicvJSZ3aWR0aEdGYXcvJStyb3dzcGFjaW5nR1EmMS4wZXhGJy8lLmNvbHVtbnNwYWNpbmdHUSQyZW1GJy8lKXJvd2xpbmVzR1Elbm9uZUYnLyUsY29sdW1ubGluZXNHRlx4LyUmZnJhbWVHRlx4LyUtZnJhbWVzcGFjaW5nR1EsMC40ZW1+MC41ZXhGJy8lKmVxdWFscm93c0dGPS8lLWVxdWFsY29sdW1uc0dGPS8lLWRpc3BsYXlzdHlsZUdGPS8lJXNpZGVHUSZyaWdodEYnLyUwbWlubGFiZWxzcGFjaW5nR1EmMC44ZW1GJ0Y5L0krbXNlbWFudGljc0dGJFEqcGllY2V3aXNlRicvJSVvcGVuR1EnJmxjdWI7RicvJSZjbG9zZUdGX3FGYHktRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk1GX29GOQ==

Haar expansion of a function

The HaarE(f, x = a..b, n) calling sequence computes the Haar series expansion

of the expression f with respect to the variable x on the interval from a to b as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

It returns list of n Haar expansions of function f(x) for "terms of expansion" n=1,2,..,n.

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

Walsh functions

The Walsh(n, j, x, opt) calling sequence computes the j-th Walsh function

n - the order of the Walsh function 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.

j - the Walsh function number (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).

x - the argument of Walsh function. opt - optional arranged order of the set of Walsh functions. It is used as follows.

order=Walsh - sequency (or Walsh) order, order=Paley - dyadic (or Paley) order, order=Hadamard - natural (or Hadamard) order .

By default opt is equal to order=Walsh.

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

Walsh expansion of a function

The WalshE(f, x = a..b, n) calling sequence computes the Walsh series expansion

of the expression f with respect to the variable x on the interval from a to b as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

It returns list of n Walsh expansions of function f(x) for "terms of expansion" n=1,2,..,n.

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

List of Slant functions

The Slant(n) calling sequence computes the list of n Slant functions.

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

Slant expansion of a function

The SlantE(f, x = a..b, n) calling sequence computes the Slant series expansion of the expression f with respect to the variable x on the interval from a to b as folows:

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

fLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbW9HRiQ2LVEqJkVsZW1lbnQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkMtSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJMRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRidGL0ZNRlAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUZKNiNRIUYnLUkobWZlbmNlZEdGJDYlLUYjNictRko2JVEiYUYnRk1GUC1GLDYtUSIsRidGL0YyL0Y2Rk9GN0Y5RjtGPUY/L0ZCUSYwLjBlbUYnL0ZFUSwwLjMzMzMzMzNlbUYnLUZKNiVRImJGJ0ZNRlAvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRi9GLy8lJW9wZW5HUSJbRidGW3BGLw== - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYnUSJuRicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR0Y2LyUsbWF0aHZhcmlhbnRHUSxib2xkLWl0YWxpY0YnLyUrZm9udHdlaWdodEdRJWJvbGRGJ0Y3L0Y6USdpdGFsaWNGJ0YrLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy9GOlEnbm9ybWFsRic=.

It returns list of n Slant expansions of function f(x) for terms of expansion n=1,2,..,n.

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

List of Piece-Linear-Quadratic functions

The PieceLQ(n) calling sequence computes the list of n Piece-Linear-Quadratic functions.

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

Piece-Linear-Quadratic expansion of a function

The PieceLQE(f, x = a..b, n) calling sequence computes the Piece-Linear-Quadratic series expansion of the expression f with respect to the variable x on the interval from a to b as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a, b - endpoints of the interval on which expansion is taken.

It returns list of n Piece-Linear-Quadratic expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Generalized Laguerre polynomials expansion of a function

The LaguerreE(f, x, a, d, n, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EnJiM5NDU7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGN0YvLyUrZm9yZWdyb3VuZEdRLVs1MSwxNTMsMTAyXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EwSGVscH5NYXBsZX5OYW1lRidGNUY4) calling sequence computes the Generalized Laguerre polynomials series expansion of the expression f with respect to the variable x on the interval from a to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RIn5GJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a - left endpoint of the semi-infinite interval on which expansion is taken.

d>0 - scale parameter.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

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parameter of the Generalized Laguerre polynomial.

It returns list of Generalized Laguerre polynomials expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Generalized Laguerre functions expansion of a function

The LaguerreFE(f, x, a, d, n, LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYoLUkjbWlHRiQ2J1EnJiM5NDU7RicvJSVib2xkR1EldHJ1ZUYnLyUnaXRhbGljR1EmZmFsc2VGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGN0YvLyUrZm9yZWdyb3VuZEdRLVs1MSwxNTMsMTAyXUYnLyUwZm9udF9zdHlsZV9uYW1lR1EwSGVscH5NYXBsZX5OYW1lRidGNUY4) calling sequence computes the Generalized Laguerre functions series expansion of the expression f with respect to the variable x on the interval from a to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RIn5GJ0YvRjJGNUY3RjlGO0Y9Rj9GQUZERi8=as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a - left endpoint of the semi-infinite interval on which expansion is taken.

d>0 - scale parameter.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

It returns list of Generalized Laguerre functions expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Hermite polynomials expansion of a function

The HermiteE(f, x, a, d, n) calling sequence computes the Hermite polynomials series expansion of the expression f with respect to the variable x on the interval from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2JC1JI21pR0YkNiVRKCYjODczNDtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGLy1GSTYjUSFGJ0Yv to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= as folows:

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY8LUkjbWlHRiQ2JlEiZkYnLyUlc2l6ZUdRIzEwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkobWZlbmNlZEdGJDYlLUYjNictRiw2JlEieEYnRi9GMkY1Ri8vJSlyZWFkb25seUdGNC8lMGZvbnRfc3R5bGVfbmFtZUdRKjJEfk91dHB1dEYnL0Y2USdub3JtYWxGJ0YvRkUtSSNtb0dGJDYuUSkmYXBwcm94O0YnRi9GRS8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGTS8lKXN0cmV0Y2h5R0ZNLyUqc3ltbWV0cmljR0ZNLyUobGFyZ2VvcEdGTS8lLm1vdmFibGVsaW1pdHNHRk0vJSdhY2NlbnRHRk0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0Zmbi1JJm1mcmFjR0YkNigtSSNtbkdGJDYkUSIxRidGRS1GIzYtLUYsNiVRImRGJ0YyRjUtRkg2LVEifkYnRkVGS0ZORlBGUkZURlZGWC9GZW5RJjAuMGVtRicvRmhuRmlvLUkmbXNxcnRHRiQ2Iy1GLDYlUSUmcGk7RicvRjNGTUZFLUZINi1RMSZJbnZpc2libGVUaW1lcztGJ0ZFRktGTkZQRlJGVEZWRlhGaG9Gam8tSSVtc3VwR0YkNiUtRl1vNiRRIjJGJ0ZFLUYsNiVRImlGJ0YyRjUvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRmJwRltxLUZINi1RIiFGJ0ZFRktGTkZQRlJGVEZWRlgvRmVuUSwwLjExMTExMTFlbUYnL0ZobkZlcS8lK2V4ZWN1dGFibGVHRjQvRkNRKTJEfklucHV0RidGRS8lLmxpbmV0aGlja25lc3NHUSIxRicvJStkZW5vbWFsaWduR1EnY2VudGVyRicvJSludW1hbGlnbkdGYHIvJSliZXZlbGxlZEdGTS1JK211bmRlcm92ZXJHRiQ2Jy1GSDYuUSYmU3VtO0YnRkUvSSttc2VtYW50aWNzR0YkUSZpbmVydEYnRktGTi9GUUY0RlIvRlVGNC9GV0Y0RlhGaG8vRmhuUSwwLjE2NjY2NjdlbUYnLUYjNihGW3EtRkg2LVEiPUYnRkVGS0ZORlBGUkZURlZGWEZaRmduLUZdbzYkUSIwRidGRUZncUZpcUZFLUYjNictRiw2JVEibkYnRjJGNS1GSDYtUSgmbWludXM7RidGRUZLRk5GUEZSRlRGVkZYL0ZlblEsMC4yMjIyMjIyZW1GJy9GaG5GZHRGXG9GMkY1LyUnYWNjZW50R0ZNLyUsYWNjZW50dW5kZXJHRk0tSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJDUuMEYnLyUmZGVwdGhHRl91LyUqbGluZWJyZWFrR1ElYXV0b0YnLUYsNiVRIkhGJ0YyRjUtRjk2JC1GIzYoRltxLUZINi1RIixGJ0ZFRksvRk9GNEZQRlJGVEZWRlhGaG8vRmhuUSwwLjMzMzMzMzNlbUYnLUZqbjYoLUYjNictRiw2JUY/RjJGNUZgdC1GLDYlUSJhRidGMkY1RjJGNS1GIzYlRmJvRjJGNUZbckZeckZhckZjckZncUZpcUZFRkVGYnAtSShtc3Vic3VwR0YkNictRkg2LlEmJmludDtGJ0ZFRltzRktGTkZQRlJGVEZWRlhGaG9Gam8tRiM2Jy1GSDYtUSomdW1pbnVzMDtGJ0ZFRktGTkZQRlJGVEZWRlhGY3RGZXQtRiw2JVEoJmluZmluO0YnRjJGNUZncUZpcUZFRlt4L0ZfcVEiMkYnLyUvc3Vic2NyaXB0c2hpZnRHRmBxLUYsNiVGLkYyRjUtRjk2JC1GIzYmRml2RmdxRmlxRkVGRS1GZnA2JS1GSDYtUS8mRXhwb25lbnRpYWxFO0YnRkVGS0ZORlBGUkZURlZGWEZob0ZmcS1GIzYnRmh3LUZmcDYlLUY5NiQtRiM2JkZldkZncUZpcUZFRkVGaHBGXnFGZ3FGaXFGRUZecUZicEZicEZodUZbdi1GW3U2JkZddS9GYXVRJjAuM2VtRidGY3VGZXUtRkg2LlEwJkRpZmZlcmVudGlhbEQ7RidGRUZbc0ZLRk5GUEZSRlRGVkZYRmhvRmpvRml2RmVvLUZINi1RIi5GJ0ZFRktGTkZQRlJGVEZWRlhGaG9Gam9GL0ZARkJGRQ==

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a - shift parameter.

d>0 - scale parameter.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

It returns list of Hermite polynomials expansions of function f(x) for terms of expansion n=1,2,..,n.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZgcS1JI21pR0YkNiVRKUhlcm1pdGVFRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtRjY2L1ElcHJvY0YnLyUlYm9sZEdGMS9GM1ElYm9sZEYnLyUrZm9udHdlaWdodEdGVUY7Rj5GQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZORlktSShtZmVuY2VkR0YkNiQtRiM2LS1GLDYlUSJmRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkhGWC9GTlEsMC4zMzMzMzMzZW1GJy1GLDYlUSJ4RidGL0YyRl1vLUYsNiVRImFGJ0YvRjJGXW8tRiw2JVEiZEYnRi9GMkZdby1GLDYlUSJuRidGL0YyLyUrZXhlY3V0YWJsZUdGPUY5RjktRiw2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuNWVtRicvJSZkZXB0aEdGaXAvJSpsaW5lYnJlYWtHUTFmaXJzdHByb2NuZXdsaW5lRictRjY2L1EmbG9jYWxGJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWi1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRlhGWi1GLDYlUSJpRidGL0YyRl1vLUYsNiVRInNGJ0YvRjJGXW8tRiw2JVEiTEYnRi9GMi1GNjYtUSI7RidGOUY7RmBvRkBGQkZERkZGSEZYRk1GZXEtRiw2JVEld2l0aEYnRi9GMi1GZm42JC1GIzYnLUYsNiVRKm9ydGhvcG9seUYnRi9GMkZdby1GLDYlUSJIRidGL0YyRl9wRjlGOUZhckZkcEZbci1GNjYtUSM6PUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSNtbkdGJDYkUSIwRidGOUZhckZeckZhcy1GZm42Ji1GIzYlRmFwRl9wRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZhckZkcC1GNjYvUSRmb3JGJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZlcUZlcUZocUZlcUZlcS1GNjYvUSVmcm9tRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGZXFGZXFGZHNGZXFGZXEtRjY2L1EjdG9GJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZlcUZlcUZccEZlcS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GX3UtRmVzNiRRIjFGJ0Y5RmVxRmVxLUY2Ni9RI2RvRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlotRmVwNiZGZ3BGanBGXXEvRmBxUTZpbmNyZWFzZWluZGVudG5ld2xpbmVGJ0ZbckY1RltyLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGXnVGYHUtSSVtc3ViR0YkNiUtRjY2LkZgc0Y5L0krbXNlbWFudGljc0dGJFEpSGVybWl0ZUhGJ0Y7Rj5GQEZCRkRGRkZIRlhGWi1GIzYkRmhxRjkvJS9zdWJzY3JpcHRzaGlmdEdRIjBGJy1GZm42JC1GIzYkLUkmbWZyYWNHRiQ2KC1GIzYnRmNvLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGXnVGYHVGZm9GL0YyLUYjNiVGaW9GL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0ZeeC8lKWJldmVsbGVkR0Y9RjlGOUZlcS1GLDYlUSZldmFsZkYnRi9GMi1GZm42JC1GIzYwLUZgdzYoLUYjNiVGYXVGL0YyLUYjNi1GaW9GZXEtSSZtc3FydEdGJDYjLUYjNiQtRiw2JVElJnBpO0YnL0YwRj1GOUY5RmVxLUklbXN1cEdGJDYlLUZlczYkUSIyRidGOUZmdi8lMXN1cGVyc2NyaXB0c2hpZnRHRmp2RmVxRmVxRmhxLUY2Ni1RIiFGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMTExMTExMWVtRicvRk5GZXpGL0YyRml3Rlx4Rl94RmF4RmVxLUkobXN1YnN1cEdGJDYnLUY2Ni1RJiZpbnQ7RidGOUY7Rj4vRkFGMUZCL0ZFRjFGRkZIRlhGWi1GIzYpRlt1LUYjNiUtRiw2JVEoJiM4NzM0O0YnRi9GMkZfcEY5RmFwRi8vJStmb3JlZ3JvdW5kR1EsWzEyOCwwLDEyOF1GJy8lLHBsYWNlaG9sZGVyR0YxRjItRiM2J0ZhcEZhW2xGYXBGL0YyRl96Rmh2RmpuRmVxLUZqeTYlLUY2Ni1RLyZFeHBvbmVudGlhbEU7RidGOUY7Rj5GQEZCRkRGRkZIRlhGZnotRiM2JUZbdS1Gank2JS1GZm42JC1GIzYkLUZgdzYoLUYjNidGY29GZHdGZm9GX3BGOUZnd0Zpd0ZceEZfeEZheEY5RjktRiM2JEZcekY5Rl96RjlGX3pGZXEtRl92NiVGYXYtRiM2J0ZocUYvRmZbbEZpW2xGMkZodi1GZm42JC1GIzYlRl93Ri9GMkY5RmVxLUY2Ni1RMCZEaWZmZXJlbnRpYWxEO0YnRjlGO0Y+RkBGQkZERkZGSEZYRlpGY29GX3BGOUY5RmFyRmVxLUZlcDYmRmdwL0ZbcVEmMC4wZW1GJ0ZdcS9GYHFRKG5ld2xpbmVGJ0ZlcUZlcUZlcUZlcUZlcUZlcUZlcUZlcUZlcUZlcUZlcUZlcUZlcUZeckZhcy1GZm42Ji1GIzYoLUYsNiVRI29wRidGL0YyLUZmbjYkLUYjNiVGXnJGX3BGOUY5Rl1vRltyRl9wRjlGOUZcdEZfdEZhckZbXmwtRmVwNiZGZ3BGXV5sRl1xL0ZgcVElYXV0b0YnLUZlcDYmRmdwRmpwRl1xL0ZgcVE2ZGVjcmVhc2VpbmRlbnRuZXdsaW5lRidGZXFGZXFGZXFGZXEtRjY2L1EkZW5kRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGZXFGZHVGYF9sLUY2Ni5GY3JGX3BGOUY7RmBvRkBGQkZERkZGSEZYRk1GW15sRlxfbC1GNjYwRmZfbEZSRl9wRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWi1GNjYuRmdxRl9wRjlGO0Y+RkBGQkZERkZGSEZYRlotRjY2MEZRRlJGX3BGVEZWRjtGPkZARkJGREZGRkhGWEZaLUY2Ni5RIjpGJ0ZfcEY5RjtGPkZARkJGREZGRkhGSkZNRl9wRjk=

Hermite functions expansion of a function

The HermiteFE(f, x, a, d, n) calling sequence computes the Hermite functions series expansion of the expression f with respect to the variable x on the interval from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2JC1JI21pR0YkNiVRKCYjODczNDtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGLy1GSTYjUSFGJ0Yv to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= as folows:

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

fLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJkVsZW1lbnQ7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkMtSSVtc3VwR0YkNiUtSSNtaUdGJDYlUSJMRicvJSdpdGFsaWNHUSV0cnVlRicvRjBRJ2l0YWxpY0YnLUYjNiUtSSNtbkdGJDYkUSIyRidGL0ZNRlAvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnLUkobWZlbmNlZEdGJDYkLUYjNiUtRko2JVEoJiM4NDc3O0YnL0ZORjRGLy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGL0YvRl5vRi8= - the algebraic expression representing the function. x - the variable name appearing in f.

a - shift parameter.

d>0 - scale parameter.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients n.

It returns list of Hermite functions expansions of function f(x) for terms of expansion n=1,2,..,n.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZicS1JI21pR0YkNiVRKkhlcm1pdGVGRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni9RJXByb2NGJy8lJWJvbGRHRjEvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlVGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZZLUkobWZlbmNlZEdGJDYkLUYjNiwtRiw2JVEiZkYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRlgvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRi9GMkZdby1GLDYlUSJhRidGL0YyRl1vLUYsNiVRImRGJ0YvRjJGXW8tRiw2JVEibkYnRi9GMkY5RjktRiw2I1EhRictSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuNWVtRicvJSZkZXB0aEdGZ3AvJSpsaW5lYnJlYWtHUTFmaXJzdHByb2NuZXdsaW5lRictRjY2L1EmbG9jYWxGJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWi1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRlhGWi1GLDYlUSJpRidGL0YyRl1vLUYsNiVRInNGJ0YvRjJGXW8tRiw2JVEiTEYnRi9GMi1GNjYtUSI7RidGOUY7RmBvRkBGQkZERkZGSEZYRk1GY3EtRiw2JVEld2l0aEYnRi9GMi1GZm42JC1GIzYmLUYsNiVRKm9ydGhvcG9seUYnRi9GMkZdby1GLDYlUSJIRidGL0YyRjlGOUZfckZicEZpcS1GNjYtUSM6PUYnRjlGO0Y+RkBGQkZERkZGSEZKRk0tSSNtbkdGJDYkUSIwRidGOUZfckZcckZfcy1GZm42Ji1GIzYkRl9wRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZfckZicC1GNjYvUSRmb3JGJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZjcUZjcUZmcUZjcUZjcS1GNjYvUSVmcm9tRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGY3FGY3FGYnNGY3FGY3EtRjY2L1EjdG9GJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZjcUZjcUZccEZjcS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkgvRktRLDAuMjIyMjIyMmVtRicvRk5GXXUtRmNzNiRRIjFGJ0Y5RmNxRmNxLUY2Ni9RI2RvRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlotRmNwNiZGZXBGaHBGW3EvRl5xUTZpbmNyZWFzZWluZGVudG5ld2xpbmVGJ0ZpcUY1RmlxLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGXHVGXnUtSSVtc3VwR0YkNiUtRjY2LVEvJkV4cG9uZW50aWFsRTtGJ0Y5RjtGPkZARkJGREZGRkhGWC9GTlEsMC4xMTExMTExZW1GJy1GIzYnRml0LUkmbWZyYWNHRiQ2KEZfdS1GIzYkLUZjczYkUSIyRidGOUY5LyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zjdy8lKWJldmVsbGVkR0Y9RmNxLUZddjYlLUZmbjYkLUYjNiQtRmd2NigtRiM2JkZjby1GNjYtUSgmbWludXM7RidGOUY7Rj5GQEZCRkRGRkZIRlx1Rl51RmZvRjktRiM2JEZpb0Y5Rl53RmF3RmR3RmZ3RjlGOUZpdi8lMXN1cGVyc2NyaXB0c2hpZnRHUSIwRidGOUZneEZjcS1JJW1zdWJHRiQ2JS1GNjYuRl5zRjkvSSttc2VtYW50aWNzR0YkUSlIZXJtaXRlSEYnRjtGPkZARkJGREZGRkhGWEZaLUYjNiRGZnFGOS8lL3N1YnNjcmlwdHNoaWZ0R0ZpeEZqd0ZjcS1GLDYlUSZldmFsZkYnRi9GMi1GZm42JC1GIzYvLUZndjYoLUYjNiRGX3VGOS1GIzYsRmlvRmNxLUkmbXNxcnRHRiQ2Iy1GIzYkLUYsNiVRJSZwaTtGJy9GMEY9RjlGOUZjcS1GXXY2JUZbd0ZieUZneEZjcUZjcUZmcS1GNjYtUSIhRidGOUY7Rj5GQEZCRkRGRkZIL0ZLRmN2RmJ2RjlGXndGYXdGZHdGZndGY3EtSShtc3Vic3VwR0YkNictRjY2LVEmJmludDtGJ0Y5RjtGPi9GQUYxRkIvRkVGMUZGRkhGWEZaLUYjNiZGaXQtRiM2JC1GLDYlUSgmaW5maW47RidGL0YyRjlGX3BGOS1GIzYmRl9wRlxcbEZfcEY5Rmd4RmR5RmpuRmNxLUZddjYlRl92LUYjNidGaXQtRmd2NihGX3UtRiM2JUZbd0YvRjJGXndGYXdGZHdGZndGY3FGaHdGOUZneEZjcUZqeEZqd0ZjcS1GNjYtUTAmRGlmZmVyZW50aWFsRDtGJ0Y5RjtGPkZARkJGREZGRkhGWEZaRmNvRjlGOUZfckZjcS1GY3A2JkZlcC9GaXBRJjAuMGVtRidGW3EvRl5xUShuZXdsaW5lRidGY3FGY3FGY3FGY3FGY3FGY3FGY3FGY3FGY3FGY3FGY3FGY3FGY3FGXHJGX3MtRmZuNiYtRiM2Jy1GLDYlUSNvcEYnRi9GMi1GZm42JC1GIzYkRlxyRjlGOUZdb0ZpcUY5RjlGanNGXXRGX3JGXl1sLUZjcDYmRmVwRmBdbEZbcS9GXnFRJWF1dG9GJy1GY3A2JkZlcEZocEZbcS9GXnFRNmRlY3JlYXNlaW5kZW50bmV3bGluZUYnRmNxRmNxRmNxRmNxLUY2Ni9RJGVuZEYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRmNxRmJ1RmNebC1GNjYuRmFyLyUrZXhlY3V0YWJsZUdGPUY5RjtGYG9GQEZCRkRGRkZIRlhGTUZeXWwtRjY2LkZlcUZcX2xGOUY7Rj5GQEZCRkRGRkZIRlhGWi1GNjYwRmlebEZSRlxfbEZURlZGO0Y+RkBGQkZERkZGSEZYRlpGXl9sLUY2NjBGUUZSRlxfbEZURlZGO0Y+RkBGQkZERkZGSEZYRlotRjY2LlEiOkYnRlxfbEY5RjtGPkZARkJGREZGRkhGSkZNRlxfbEY5

Orthogonal Rational functions

The Rat(j, x) calling sequence computes the j-th Orthogonal Rational function.

x - the argument of the function.

This functions are orthonormal on the interval 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.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2JVEkUmF0RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVEqJmNvbG9uZXE7RicvRjNRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y9LyUpc3RyZXRjaHlHRj0vJSpzeW1tZXRyaWNHRj0vJShsYXJnZW9wR0Y9LyUubW92YWJsZWxpbWl0c0dGPS8lJ2FjY2VudEdGPS8lJ2xzcGFjZUdRLDAuMjc3Nzc3OGVtRicvJSdyc3BhY2VHRkwtSShtZmVuY2VkR0YkNiQtRiM2Ji1GLDYlUSJqRidGL0YyLUY2Ni1RIixGJ0Y5RjsvRj9GMUZARkJGREZGRkgvRktRJjAuMGVtRicvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRi9GMkY5RjktRjY2LVEoJnNyYXJyO0YnRjlGO0Y+RkBGQkZERkZGSEZlbi9GTkZmbi1JJm1mcmFjR0YkNigtRiM2JS1GLDYjUSFGJy1JJW1zdXBHRiQ2JS1GUDYkLUYjNigtSSNtbkdGJDYkUSIxRidGOS1GNjYtUSIrRidGOUY7Rj5GQEZCRkRGRkZIL0ZLUSwwLjIyMjIyMjJlbUYnL0ZORmdwLUYsNiVRIklGJ0YvRjItRjY2LVEifkYnRjlGO0Y+RkBGQkZERkZGSEZlbkZfb0ZpbkY5RjktRiM2JEZURjkvJTFzdXBlcnNjcmlwdHNoaWZ0R1EiMEYnRjktRiM2KEZlby1JJm1zcXJ0R0YkNiMtRiM2JC1GLDYlUSUmcGk7RicvRjBGPUY5RjlGXHFGXHEtRmlvNiUtRlA2JC1GIzYoRl9wLUY2Ni1RKCZtaW51cztGJ0Y5RjtGPkZARkJGREZGRkhGZnBGaHBGaXBGXHFGaW5GOUY5LUYjNiZGVEZjcEZfcEY5RmFxRjkvJS5saW5ldGhpY2tuZXNzR1EiMUYnLyUrZGVub21hbGlnbkdRJ2NlbnRlckYnLyUpbnVtYWxpZ25HRl9zLyUpYmV2ZWxsZWRHRj0tRjY2LVEiOkYnRjlGO0Y+RkBGQkZERkZGSEZKRk0vJStleGVjdXRhYmxlR0Y9Rjk=

Orthogonal Rational expansion of a function

The RatE(f, x, a, d, n) calling sequence computes the Orthogonal Rational series expansion of the expression f with respect to the variable x on the interval from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2JC1JI21pR0YkNiVRKCYjODczNDtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGLy1GSTYjUSFGJ0Yv to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a - shift parameter.

d>0 - scale parameter.

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients 2n.

It returns list of Orthogonal Rational expansions of function f(x) for terms of expansion n=1,2,..,n.

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

Generalized sinc functions

The Gsinc(d, a, m, j, x) calling sequence computes the j-th Generalised sinc function.

a - shift parameter.

d>0 - scale parameter.

m\342\210\210\342\204\225 - rolloff factor (for m=2 and m=3 the Generalised sinc functions are not orthogonal),

x - the argument of the function.

If m=1 then the procedure returns sinc function.

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

Generalized sinc expansion of a function

The GsincE(f, x, a, d, m, n) calling sequence computes the Generalized sinc series expansion of the expression f with respect to the variable x on the interval from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2JS1JI21pR0YkNiVRKCYjODczNDtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRicvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRi8tRkk2I1EhRidGUUYv to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2I1EhRictRiM2JS1GLDYlUSgmIzg3MzQ7RicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy9GOFEnbm9ybWFsRidGK0Y6Rj0= as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a - shift parameter.

d>0 - scale parameter.

m\342\210\210\342\204\225LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbW9HRiQ2LVEifkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLUYsNi1RKiZ1bWludXMwO0YnRi9GMkY1RjdGOUY7Rj1GPy9GQlEsMC4yMjIyMjIyZW1GJy9GRUZKRisvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRi8=rolloff factor (if m=2 or m=3 the expansions is not orthogonal).

If m=1 then the procedure returns sinc expansion (Whittaker-Shannon-Kotelnikov series expansion).

n - the maximal number of expansion terms that correspond to the number of the expansion coefficients 2n-1.

It returns list of n Generalized sinc expansions of function f(x) for terms of expansion n=1,2,..,n.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzZbcy1JI21pR0YkNiVRJ0dzaW5jRUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1JI21vR0YkNi1RKiZjb2xvbmVxO0YnL0YzUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGPS8lKXN0cmV0Y2h5R0Y9LyUqc3ltbWV0cmljR0Y9LyUobGFyZ2VvcEdGPS8lLm1vdmFibGVsaW1pdHNHRj0vJSdhY2NlbnRHRj0vJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZMLUY2Ni9RJXByb2NGJy8lJWJvbGRHRjEvRjNRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRlVGO0Y+RkBGQkZERkZGSC9GS1EmMC4wZW1GJy9GTkZZLUkobWZlbmNlZEdGJDYkLUYjNi4tRiw2JVEiZkYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIRlgvRk5RLDAuMzMzMzMzM2VtRictRiw2JVEieEYnRi9GMkZdby1GLDYlUSJhRidGL0YyRl1vLUYsNiVRImRGJ0YvRjJGXW8tRiw2JVEibUYnRi9GMkZdby1GLDYlUSJuRidGL0YyRjlGOS1GNjYtUSJ+RidGOUY7Rj5GQEZCRkRGRkZIRlhGWi1JJ21zcGFjZUdGJDYmLyUnaGVpZ2h0R1EmMC4wZXhGJy8lJndpZHRoR1EmMC4wZW1GJy8lJmRlcHRoR0ZqcC8lKmxpbmVicmVha0dRKG5ld2xpbmVGJy1GZnA2JkZocEZbcUZecS9GYXFRJWF1dG9GJy1GNjYvUSZsb2NhbEYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRmJwLUYsNiVRImlGJ0YvRjJGXW8tRiw2JVEic0YnRi9GMkZdby1GLDYlUSJMRidGL0YyLUY2Ni1RIjtGJ0Y5RjtGYG9GQEZCRkRGRkZIRlhGTS1GZnA2JkZocC9GXHFRJjAuNWVtRidGXnEvRmFxUTFmaXJzdHByb2NuZXdsaW5lRidGYHItRjY2LVEjOj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUZmbjYmLUYjNiQtRiw2I1EhRidGOUY5LyUlb3BlbkdRIltGJy8lJmNsb3NlR1EiXUYnRmNyRmZyRl1yRlxzLUkjbW5HRiQ2JFEiMEYnRjlGY3JGZXAtRjY2L1EkZm9yRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGYnBGanFGYnBGYnAtRjY2L1ElZnJvbUYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRmJwRmJwRlx0RmJwRmJwLUY2Ni9RI3RvRidGUkZURlZGO0Y+RkBGQkZERkZGSEZYRlpGYnBGX3AtRjY2LVEoJm1pbnVzO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZddS1GXXQ2JFEiMUYnRjlGYnBGYnAtRjY2L1EjZG9GJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZlcEZicEZicEZicEZicEZdckY1Rl1yLUY2Ni1RIitGJ0Y5RjtGPkZARkJGREZGRkhGXHVGXnUtRiw2JVElZXZhbEYnRi9GMi1GZm42JC1GIzYrRmpuRl1vRmNvLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUkmbWZyYWNHRiQ2KC1GIzYpRmpxLUY2Ni1RJyZzZG90O0YnRjlGO0Y+RkBGQkZERkZGSEZYRlpGaW9GZ3YtRmZuNiQtRiM2J0ZccEZldUZfdS8lK2V4ZWN1dGFibGVHRj1GOUY5Rl53RjktRiM2JS1GXXQ2JFEiMkYnRjlGL0YyLyUubGluZXRoaWNrbmVzc0dRIjFGJy8lK2Rlbm9tYWxpZ25HUSdjZW50ZXJGJy8lKW51bWFsaWduR0Zqdy8lKWJldmVsbGVkR0Y9RmV1RmZvRl53RjlGOUZndkZicC1GLDYlUSZHc2luY0YnL0YwRj1GOS1GZm42JC1GIzYtRmlvRl1vRmZvRl1vRlxwRl1vRmpxRl1vRmNvRl53RjlGOUZjckZicEZlcEZicEZicEZicEZicC1GNjYvUSNpZkYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRmJwRmpxLUY2Ni1RIj5GJ0Y5RjtGPkZARkJGREZGRkhGSkZNRlx0RmJwLUY2Ni9RJXRoZW5GJ0ZSRlRGVkY7Rj5GQEZCRkRGRkZIRlhGWkZicEZlcEZicEZicEZicEZicEZicEZicEZdckY1Rl1yRmV1Rmh1LUZmbjYkLUYjNipGam5GXW9GY29GX3YtRmN2NigtRiM2KS1GNjYtUSomdW1pbnVzMDtGJ0Y5RjtGPkZARkJGREZGRkhGXHVGXnVGanFGZ3ZGaW9GZ3YtRmZuNiQtRiM2JkZccEZldUZfdUY5RjlGOS1GIzYkRmJ3RjlGZXdGaHdGW3hGXXhGZXVGZm9GOUY5Rmd2RmJwRl94LUZmbjYkLUYjNi1GaW9GXW9GZm9GXW9GXHBGXW9GaHlGanFGXW9GY29GOUY5RmNyRmVwRmJwRmJwRmJwRmJwRmJwRmJwLUY2Ni9RJGVuZEYnRlJGVEZWRjtGPkZARkJGREZGRkhGWEZaRmJwRmd4RmNyRmVwRmJwRmJwRmJwRmJwRmJwRmByRjUtRmZuNiYtRiM2Jy1GLDYlUSNvcEYnRi9GMi1GZm42JC1GIzYkRmByRjlGOUZdb0ZdckY5RjlGZnNGaXNGY3JGZXBGZXpGYnBGYnVGY3JGZXAtRjY2LkZkcEZed0Y5RjtGPkZARkJGREZGRkhGWEZaLUY2NjBGZ3pGUkZed0ZURlZGO0Y+RkBGQkZERkZGSEZYRlpGY1tsLUY2NjBGUUZSRl53RlRGVkY7Rj5GQEZCRkRGRkZIRlhGWi1GNjYuUSI6RidGXndGOUY7Rj5GQEZCRkRGRkZIRkpGTUZed0Y5

Sinc Wavelets (Shannon wavelets)

The Sincwave(n, j, x) calling sequence computes the j-th Sinc Wavelet

of order (scale) n on interval (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).

nLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2L1EoJmlzaW52O0YnLyUlYm9sZEdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZILUkjbWlHRiQ2JVEoJiM4NDg0O0YnLyUnaXRhbGljR0Y5L0YzUSdub3JtYWxGJ0ZR - the order of the Sinc Wavelet (scale of the wavelet)LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEiLkYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8=

jLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2L1EoJmlzaW52O0YnLyUlYm9sZEdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZILUkjbWlHRiQ2JVEoJiM4NDg0O0YnLyUnaXRhbGljR0Y5L0YzUSdub3JtYWxGJ0ZR - the Sinc Wavelet number (shift of the wavelet).

x - the argument of Sinc Wavelet.

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

Sinc Wavelets expansion of a function

The SincwaveE(f, x , a, d, n) calling sequence computes the Sinc Wavelet series expansion

of the expression f with respect to the variable x on the interval from LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LVEqJnVtaW51czA7RicvJSxtYXRodmFyaWFudEdRJ25vcm1hbEYnLyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y0LyUpc3RyZXRjaHlHRjQvJSpzeW1tZXRyaWNHRjQvJShsYXJnZW9wR0Y0LyUubW92YWJsZWxpbWl0c0dGNC8lJ2FjY2VudEdGNC8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHRkMtRiM2JC1JI21pR0YkNiVRKCYjODczNDtGJy8lJ2l0YWxpY0dRJXRydWVGJy9GMFEnaXRhbGljRidGLy1GSTYjUSFGJ0Yv to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYkLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDRi8= as folows:

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 - the algebraic expression representing the function. x - the variable name appearing in f.

a - initial shift parameter.

d>0 - initial scale parameter.

n - the maximal number of "expansion terms" that correspond to the number of the expansion coefficients 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.

It returns list of n Sinc Wavelet expansions of function f(x) for "terms of expansion" n=1,2,..,n.

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Selection of function and interval of expansion</Text-field>

Functions for expansion:

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

Enter maximal number of expansion terms: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUklbXN1YkdGJDYlLUkjbWlHRiQ2JlEibkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUnb3BhcXVlR0Y0LyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy1GIzYnLUYvNiZRJG1heEYnL0YzUSZmYWxzZUYnRjUvRjhRJ25vcm1hbEYnRjIvJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRjVGNy8lL3N1YnNjcmlwdHNoaWZ0R1EiMEYnRkNGNUZB=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # nmax:=Do(%TextArea0); end use;

Enter interval for expansion from a to b: a=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea1); end use; b=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # b:=Do(%TextArea2); end use;

Select function for expansion:

use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; 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

Reading of the selected parameters

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Fourier expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

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

<Text-field style="Heading 1" layout="Heading 1">Hartley expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

<Text-field style="Heading 1" layout="Heading 1">Fourier-Bessel expansion</Text-field>

Enter the order of Bessel function 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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEidkYnLyUnaXRhbGljR1EldHJ1ZUYnLyUnb3BhcXVlR0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMi9GNVEnbm9ybWFsRic==use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # v:=Do(%TextArea3); end use;

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

List of the expansions evaluation

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

Animation of expansions

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

<Text-field style="Heading 1" layout="Heading 1">Orthogonal Rational Tangent expansion</Text-field>

Enter the form factor LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkobWZlbmNlZEdGJDYkLUYjNictSSNtaUdGJDYlUSJwRicvJSdpdGFsaWNHUSV0cnVlRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2LVElJm5lO0YnL0Y4USdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGQi8lKXN0cmV0Y2h5R0ZCLyUqc3ltbWV0cmljR0ZCLyUobGFyZ2VvcEdGQi8lLm1vdmFibGVsaW1pdHNHRkIvJSdhY2NlbnRHRkIvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZRLUkjbW5HRiQ2JFEiMEYnRj4vJStmb3JlZ3JvdW5kR1EoWzAsMCwwXUYnRj5GPkZYRj4=: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEicEYnLyUnaXRhbGljR1EldHJ1ZUYnLyUnb3BhcXVlR0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMi9GNVEnbm9ybWFsRic==use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # v:=Do(%TextArea24); end use;

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

List of the expansions evaluation

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

Animation of expansions

<Text-field style="Heading 1" layout="Heading 1">Associated Legandre expansion</Text-field>

Enter the order of Associated Legandre function (mLUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2L1EoJmlzaW52O0YnLyUlYm9sZEdRJXRydWVGJy8lLG1hdGh2YXJpYW50R1ElYm9sZEYnLyUrZm9udHdlaWdodEdGNC8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGOS8lKXN0cmV0Y2h5R0Y5LyUqc3ltbWV0cmljR0Y5LyUobGFyZ2VvcEdGOS8lLm1vdmFibGVsaW1pdHNHRjkvJSdhY2NlbnRHRjkvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZILUkjbWlHRiQ2JVEoJiM4NDg0O0YnLyUnaXRhbGljR0Y5L0YzUSdub3JtYWxGJ0ZR): LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEibUYnLyUnaXRhbGljR1EldHJ1ZUYnLyUnb3BhcXVlR0YxLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWNGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMi9GNVEnbm9ybWFsRic==use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # v:=Do(%TextArea19); end use;

If LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYnLUkjbWlHRiQ2KFEibUYnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dGMS8lJ29wYXF1ZUdGMS8lLG1hdGh2YXJpYW50R1EsYm9sZC1pdGFsaWNGJy8lK2ZvbnR3ZWlnaHRHUSVib2xkRidGL0Y0L0Y3RjtGOQ==LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPUYnLyUnb3BhcXVlR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZGLUkjbW5HRiQ2JVEiMEYnRi9GMkYvRjI= then the procedure returns Legendre polynomials expansion.

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

List of the expansions evaluation

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

OyIiIkkpaW5maW5pdHlHJSpwcm90ZWN0ZWRH

Animation of expansions

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<Text-field style="Heading 1" layout="Heading 1">Jacobi expansion</Text-field>

Enter the parameters

of the polynomials

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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUnb3BhcXVlR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMkY1=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # v:=Do(%TextArea4); end use;

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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NDY7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUnb3BhcXVlR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMkY1=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # v:=Do(%TextArea5); end use;

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSdvcGFxdWVHRi4vJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjY=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 then the procedure returns Legendre polynomials expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSdvcGFxdWVHRi4vJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjY=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 then the procedure returns Chebyshev first kind polynomials (functions) expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSdvcGFxdWVHRi4vJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjY=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 then the procedure returns Chebyshev second kind polynomials (functions) expansion.

If LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSdvcGFxdWVHRi4vJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjY=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then the procedure returns Gegenbauer polynomials (functions) expansion.

Otherwise the procedure returns Jacobi polynomials (functions) expansion.

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY5LUkjbW9HRiQ2L1EkdXNlRicvJSVib2xkR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSVib2xkRicvJStmb250d2VpZ2h0R0Y0LyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0Y5LyUpc3RyZXRjaHlHRjkvJSpzeW1tZXRyaWNHRjkvJShsYXJnZW9wR0Y5LyUubW92YWJsZWxpbWl0c0dGOS8lJ2FjY2VudEdGOS8lJ2xzcGFjZUdRJjAuMGVtRicvJSdyc3BhY2VHRkgtSSdtc3BhY2VHRiQ2Ji8lJ2hlaWdodEdRJjAuMGV4RicvJSZ3aWR0aEdRJjAuNWVtRicvJSZkZXB0aEdGUC8lKmxpbmVicmVha0dRJWF1dG9GJy1JI21pR0YkNiVRLkRvY3VtZW50VG9vbHNGJy8lJ2l0YWxpY0dGMS9GM1EnaXRhbGljRidGSy1GLDYvUSNpbkYnRi9GMkY1RjdGOkY8Rj5GQEZCRkRGRkZJLUZMNiZGTkZRRlQvRldRNmluY3JlYXNlaW5kZW50bmV3bGluZUYnLUZaNiVRJyYjOTQ1O0YnL0ZobkY5L0YzUSdub3JtYWxGJy1GLDYtUSomY29sb25lcTtGJ0Zmb0Y3RjpGPEY+RkBGQkZEL0ZHUSwwLjI3Nzc3NzhlbUYnL0ZKRlxwLUZaNiVRI0RvRidGZ25GaW4tSShtZmVuY2VkR0YkNiQtRiM2JC1GWjYlUSslVGV4dEFyZWE0RidGZ25GaW5GZm9GZm8tRiw2LVEiO0YnRmZvRjcvRjtGMUY8Rj5GQEZCRkRGRkZdcC1GWjYlUScmIzk0NjtGJ0Zlb0Zmb0Zob0ZecC1GYnA2JC1GIzYkLUZaNiVRKyVUZXh0QXJlYTVGJ0ZnbkZpbkZmb0Zmby1GWjYjUSFGJy1GTDYmRk5GUUZUL0ZXUTZkZWNyZWFzZWluZGVudG5ld2xpbmVGJy1GLDYvUSRlbmRGJ0YvRjJGNUY3RjpGPEY+RkBGQkZERkZGSS1GLDYtUSJ+RidGZm9GN0Y6RjxGPkZARkJGREZGRklGKy1GLDYtUSI6RidGZm9GN0Y6RjxGPkZARkJGREZbcEZdcC8lK2V4ZWN1dGFibGVHRjlGZm8=

<Text-field style="Heading 2" layout="Heading 2">Jacobi polynomials expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

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<Text-field style="Heading 2" layout="Heading 2">Jacobi functions expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

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LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Rect expansion</Text-field>

List of the expansions evaluation

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Animation of expansions

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<Text-field style="Heading 1" layout="Heading 1">Haar expansion</Text-field>

List of the expansions evaluation

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Animation of expansions

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<Text-field style="Heading 1" layout="Heading 1">Walsh expansion</Text-field>

List of the expansions evaluation

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Animation of expansions

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<Text-field style="Heading 1" layout="Heading 1">Slant expansion</Text-field>

List of the expansions evaluation

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Animation of expansions

<Text-field style="Heading 1" layout="Heading 1">Piece-Linear-Quadratic expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

<Text-field style="Heading 1" layout="Heading 1">Generalized Laguerre expansion on <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYqLUkjbWlHRiQ2I1EhRictSShtZmVuY2VkR0YkNictRiM2Ky1GLDYnUSJhRicvJSVzaXplR1EjMThGJy8lJ2l0YWxpY0dRJXRydWVGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRicvJSxtYXRodmFyaWFudEdRJ2l0YWxpY0YnLUkjbW9HRiQ2MFEjLi5GJ0Y3RjpGPUZALyUmZmVuY2VHUSZmYWxzZUYnLyUqc2VwYXJhdG9yR0ZJLyUpc3RyZXRjaHlHRkkvJSpzeW1tZXRyaWNHRkkvJShsYXJnZW9wR0ZJLyUubW92YWJsZWxpbWl0c0dGSS8lJ2FjY2VudEdGSS8lJ2xzcGFjZUdRLDAuMjIyMjIyMmVtRicvJSdyc3BhY2VHUSYwLjBlbUYnLUZENjBRKCZpbmZpbjtGJ0Y3RjpGPUZARkdGSkZMRk5GUEZSRlQvRldGZW5GWUY3LyUlYm9sZEdGPEY9LyUwZm9udF9zdHlsZV9uYW1lR1EqSGVhZGluZ34xRicvRkFRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRmBvRjdGPS9GQVEnbm9ybWFsRicvJSVvcGVuR1EiW0YnRjdGam5GPUZcb0Zfb0Zhbw==</Equation> </Text-field>

Functions for expansion:

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

Enter interval for expansion from a to LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYlLUkjbW9HRiQ2LVEoJmluZmluO0YnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNC8lKXN0cmV0Y2h5R0Y0LyUqc3ltbWV0cmljR0Y0LyUobGFyZ2VvcEdGNC8lLm1vdmFibGVsaW1pdHNHRjQvJSdhY2NlbnRHRjQvJSdsc3BhY2VHUSYwLjBlbUYnLyUncnNwYWNlR0ZDLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJ0Yv: a=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea7); end use;

Enter scale parameter (d>0): d=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea12); end use;

Enter the parameters of the polynomials 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: LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbWlHRiQ2JlEnJiM5NDU7RicvJSdpdGFsaWNHUSZmYWxzZUYnLyUnb3BhcXVlR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lK2ZvcmVncm91bmRHUShbMCwwLDBdRidGMkY1=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # v:=Do(%TextArea8); end use;

( if LUkjbWlHNiMvSSttb2R1bGVuYW1lRzYiSSxUeXBlc2V0dGluZ0dJKF9zeXNsaWJHRic2KFEoJmFscGhhO0YnLyUlYm9sZEdRJXRydWVGJy8lJ2l0YWxpY0dRJmZhbHNlRicvJSdvcGFxdWVHRi4vJSxtYXRodmFyaWFudEdRJWJvbGRGJy8lK2ZvbnR3ZWlnaHRHRjY=LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYmLUkjbW9HRiQ2LlEiPUYnLyUnb3BhcXVlR1EldHJ1ZUYnLyUsbWF0aHZhcmlhbnRHUSdub3JtYWxGJy8lJmZlbmNlR1EmZmFsc2VGJy8lKnNlcGFyYXRvckdGNy8lKXN0cmV0Y2h5R0Y3LyUqc3ltbWV0cmljR0Y3LyUobGFyZ2VvcEdGNy8lLm1vdmFibGVsaW1pdHNHRjcvJSdhY2NlbnRHRjcvJSdsc3BhY2VHUSwwLjI3Nzc3NzhlbUYnLyUncnNwYWNlR0ZGLUkjbW5HRiQ2JVEiMEYnRi9GMkYvRjI= then the procedure returns

Laguerre polynomials (functions) expansion)

Select function for expansion:

use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; 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

Reading of the selected parameters

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

<Text-field style="Heading 2" layout="Heading 2">Generalized Laguerre polynomials expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

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

<Text-field style="Heading 2" layout="Heading 2">Generalized Laguerre functions expansion</Text-field>

List of the expansions evaluation

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

Animation of expansions

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Hermite expansion on interval <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>

Functions for expansion:

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

Enter shift parameter: a=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea13); end use;

Select function for expansion:

use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; 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Reading of the selected parameters

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<Text-field style="Heading 2" layout="Heading 2">Hermite polynomials expansion</Text-field>

List of the expansions evaluation

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Animation of expansions

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<Text-field style="Heading 2" layout="Heading 2">Hermite functions expansion</Text-field>

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

Animation of expansions

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

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYjLUkjbWlHRiQ2I1EhRic=

<Text-field style="Heading 1" layout="Heading 1">Orthogonal Rational expansion on interval <Equation executable="false" style="2D Math" input-equation="" display="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">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</Equation></Text-field>

Functions for expansion:

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

Select function for expansion:

use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; NiYtJSdDVVJWRVNHNiQ3Ym83JCQhI2chIiIkIjImZWptd0B2eUMhIz43JCQhKjpNJVFkISIpJCIxZDtSamchKT5LISM9NyQkISxENVozXiYhIzUkIjEmKjQlb08ib1VTISM9NyQkIStsOyFcRCYhIiokIjFaPEplKGY9QSYhIz03JCQhK2InZnMqXCEiKiQiMUZgJjNpT2t2JyEjPTckJCEsRDxVM3UlISM1JCIwL2hnJCkqR0ooKSEjPDckJCEsRE01Sl0lISM1JCIyLVsrTXVcdTUiISM9NyQkISxEIUcmcEQlISM1JCIyTUc2KFssYTs5ISM9NyQkISxES3dCKyUhIzUkIjFRc2pwbUBGPSEjPDckJCEsREY7J1tQISM1JCIxXzZHYDUuYkIhIzw3JCQhKihHZihbJCEiKSQiMk8qND08IVF1MCQhIz03JCQhKzpMb2RLISIqJCIxUVQpUVxWeCVRISM8NyQkISpoZikpKkghIikkIjEpZSUpR3UoUSUpXCEjPDckJCEqOnQqUUYhIikkIjE7JHAyXW9PWSchIzw3JCQhKlJDJilbIyEiKSQiMVl4L20qUktJKSEjPDckJCEsRCNINGhBISM1JCIyYWE7MStsQi8iISM8NyQkISoiXGwhKj4hIikkIjJvbUdiSmZnTyIhIzw3JCQhKldlOnciISIpJCIyJVxwVTUmcHhyIiEjPDckJCEsRHlrXVwiISM1JCIyT1xlInkyTVVBISM8NyQkITIuKysrdXMiZjchIzskIjIuNnJAeigpKVFHISM8NyQkIS1EaHN3SDYhIzYkIjJraiJHdlczSkshIzw3JCQhMigqKioqXCN5aC4rIiEjOyQiMVUmKSoqR1BZeE8hIzs3JCQhMSgqKioqKlw7UHIoKSEjOyQiMWlsJjNvPyhmVCEjOzckJCExKCoqKipcWkQiUnYhIzskIjFYYGJwK0EwWiEjOzckJCExKCoqKlxpZVNgaSEjOyQiMTNseG86el1gISM7NyQkITJqKioqKipcaW9uXCEjPCQiMVwnendkUFwzJyEjOzckJCExJyoqKlwoRyUqcHkkISM7JCIxaSQ9SylSXlpvISM7NyQkITEnKioqKlxLLWpnIyEjOyQiMTIrSnJ6bDB4ISM7NyQkITJ1KipcN1ZNJnA+ISM8JCIxNktzaScpRzcjKSEjOzckJCEyJykqKipcUGx3SzghIzwkIjE+I3khXCNIQXYpISM7NyQkITEqKioqXFBrKSpmcCEjPCQiMWMoPWF5cHdLKiEjOzckJCExNiwrK10yQmYhIz0kIjBDcCM9ViU0JSoqISM6NyQkIjEqKSpcaSFwIVtyIyEjPCQiMUR4W3Q4JXlAKiEjOzckJCIxKikqKlw3OCM+LSchIzwkIjFLcjlhM0BaJCkhIzs3JCQiMCoqXCg9ZC5IJCohIzskIjAkUmEoKj0iKWV2ISM6NyQkIjEqKioqXDddaGo3ISM7JCIxTy1SJW94WyVvISM7NyQkIjEqKlw3YGtLJWYiISM7JCIwQkpnKFxQKT4nISM6NyQkIjEqKipcUCp5LkQ+ISM7JCIwXEN0I1skSGgmISM6NyQkIjEqKlxQTSRcZEQjISM7JCIxayVHUCUpKnkjMyYhIzs3JCQiMSoqKioqXHhna2UjISM7JCIyLnMmXGt0ci1ZISM8NyQkIjEqKioqXFA4QmlKISM7JCIxbCMqKjNqZkQoUSEjOzckJCIyKCkqKioqKioqPStRUCEjPCQiMnhlanpPSiNlSyEjPDckJCIyJikqKipcaUN4OFYhIzwkIjJgQGhdI3lOVEYhIzw3JCQiMSkqKioqXC1WJiopWyEjOyQiMj0kUnVfInprSSMhIzw3JCQiLHYpKlFLOCchIzYkIjImKmYjKkhAPiMpZSIhIzw3JCQiMS4rK11cJHBQKCEjOyQiMjM/X0ZQS080IiEjPDckJCIxKioqKipcZCV6aCcpISM7JCIxZTFbKnlAI1F1ISM8NyQkIjEnKioqKioqPmFtJSoqISM7JCIxUnEhUXZEIWZdISM8NyQkIjInKioqKlxuUU8/NiEjOyQiMldpIXBgaXRwTSEjPTckJCIyJyoqKioqXEppZ0MiISM7JCIyYkNCI3A0c3pCISM9NyQkIjIpKioqXGktI29uOCEjOyQiMiYqKmZcYHFBXzshIz03JCQiLHZ0LCQqWyIhIzUkIjJmbFF5MUtyOSIhIz03JCQiMikqKioqKlxreCRmPCEjOyQiMUZuWHR2JT41JiEjPTckJCIxKioqKioqZkcwLT8hIzokIjIlZV0jUlxMTlkjISM+NyQkIipYZzZFIyEiKSQiMmIlKkhhK0VCOCIhIz43JCQiMiYqKioqXFAvJmZcIyEjOyQiMXBNUCxnVylmJiEjPjckJCIyMisrKyJ6al9GISM7JCIxZClvLCg9Kj5mIyEjPjckJCIxKioqKlw8MzslKkghIzokIjFwKltHKG8hZkQiISM+NyQkIix2JT1pWUshIzUkIjEpPkUuQlgpKSllISM/NyQkIjImKioqKioqXCdbTVwkISM7JCIxVUYoSGIrJDNHISM/NyQkIjIlKioqKlxQTSY9diQhIzskIjFZcGZydF4kSCIhIz83JCQiMSwrK2d6cytTISM6JCIxJ28oM3MoMzM4JyEjQDckJCIrMCJRX0QlISIqJCIxSCdlMyIqb3EmRyEjQDckJCIxLCtdeDJrMlghIzokIjFrKlxRJTQqKVI4ISNANyQkIjEsKys/RWRSWiEjOiQiMVAlUkFyTjxvJyEjQTckJCIrJm8jUjBdISIqJCIyWUpEdktLKjRJISNCNyQkIipLWEpDJiEiKSQiMmV4QSM0RCt2OSEjQjckJCIsdkBSbVwmISM1JCIxaCR5VmRwWipvISNCNyQkIixEQWwjUmQhIzUkIjAoKWZcYTQoSEwhI0E3JCQiI2chIiIkIjFqN1p1eipIXyIhI0ItJSZDT0xPUkc2JiUkUkdCRyQiIzUhIiIkIiIhISIiJCIiISEiIi0lJVZJRVdHNiQ7JCEjZyEiIiQiI2chIiIlKERFRkFVTFRHLSUrQVhFU0xBQkVMU0c2Jy1JI21pRzYjL0krbW9kdWxlbmFtZUc2IkksVHlwZXNldHRpbmdHSShfc3lzbGliRzYiNjVRIng2Ii8lJ2ZhbWlseUdRITYiLyUlc2l6ZUdRIzEwNiIvJSVib2xkR1EmZmFsc2U2Ii8lJ2l0YWxpY0dRJXRydWU2Ii8lKnVuZGVybGluZUdRJmZhbHNlNiIvJSpzdWJzY3JpcHRHUSZmYWxzZTYiLyUsc3VwZXJzY3JpcHRHUSZmYWxzZTYiLyUrZm9yZWdyb3VuZEdRKFswLDAsMF02Ii8lK2JhY2tncm91bmRHUS5bMjU1LDI1NSwyNTVdNiIvJSdvcGFxdWVHUSZmYWxzZTYiLyUrZXhlY3V0YWJsZUdRJmZhbHNlNiIvJSlyZWFkb25seUdRJmZhbHNlNiIvJSljb21wb3NlZEdRJmZhbHNlNiIvJSpjb252ZXJ0ZWRHUSZmYWxzZTYiLyUraW1zZWxlY3RlZEdRJmZhbHNlNiIvJSxwbGFjZWhvbGRlckdRJmZhbHNlNiIvJTZzZWxlY3Rpb24tcGxhY2Vob2xkZXJHUSZmYWxzZTYiLyUsbWF0aHZhcmlhbnRHUSdpdGFsaWM2IlEhNiItJSVGT05URzYlJShERUZBVUxURyUoREVGQVVMVEciIzUlK0hPUklaT05UQUxHJStIT1JJWk9OVEFMRy0lJVJPT1RHNictJSlCT1VORFNfWEc2IyQiJEkiISIiLSUpQk9VTkRTX1lHNiMkIiNdISIiLSUtQk9VTkRTX1dJRFRIRzYjJCIlcTwhIiItJS5CT1VORFNfSEVJR0hURzYjJCIlUzohIiItJSlDSElMRFJFTkc2Ig==

Reading of the selected parameters

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

List of the expansions evaluation

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

Animation of expansions

LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzY1LUkjbWlHRiQ2JVEjcGZGJy8lJ2l0YWxpY0dRJXRydWVGJy8lLG1hdGh2YXJpYW50R1EnaXRhbGljRictSSNtb0dGJDYtUSomY29sb25lcTtGJy9GM1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj0vJSlzdHJldGNoeUdGPS8lKnN5bW1ldHJpY0dGPS8lKGxhcmdlb3BHRj0vJS5tb3ZhYmxlbGltaXRzR0Y9LyUnYWNjZW50R0Y9LyUnbHNwYWNlR1EsMC4yNzc3Nzc4ZW1GJy8lJ3JzcGFjZUdGTC1GLDYlUShhbmltYXRlRidGL0YyLUkobWZlbmNlZEdGJDYkLUYjNi8tRiw2JVElcGxvdEYnRi9GMi1GNjYtUSIsRidGOUY7L0Y/RjFGQEZCRkRGRkZIL0ZLUSYwLjBlbUYnL0ZOUSwwLjMzMzMzMzNlbUYnLUZTNiYtRiM2LC1GLDYlUSJmRidGL0YyLUZTNiQtRiM2JC1GLDYlUSJ4RidGL0YyRjlGOUZaRmdvLUY2Ni1RIj1GJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUY2Ni1RKiZ1bWludXMwO0YnRjlGO0Y+RkBGQkZERkZGSC9GS1EsMC4yMjIyMjIyZW1GJy9GTkZhcC1JI21uR0YkNiRRIjZGJ0Y5LUY2Ni1RIy4uRidGOUY7Rj5GQEZCRkRGRkZIRmBwL0ZORmluRmNwRjlGOS8lJW9wZW5HUSJbRicvJSZjbG9zZUdRIl1GJ0ZaLUYsNiVRIm5GJ0YvRjJGam8tRlM2Ji1GIzYoLUY2Ni1RIiRGJ0Y5RjtGPkZARkJGREZGRkhGaG5GanAtRmRwNiRRIjFGJ0Y5RmdwLUY2Ni1RIn5GJ0Y5RjtGPkZARkJGREZGRkhGaG5GanAtRiw2JVElbm1heEYnRi9GMkY5RjlGW3FGXnFGWkZeci1GLDYlUSdmcmFtZXNGJ0YvRjJGam9GYXJGOUY5LUY2Ni1RIjpGJ0Y5RjtGPkZARkJGREZGRkhGSkZNLUknbXNwYWNlR0YkNiYvJSdoZWlnaHRHUSYwLjBleEYnLyUmd2lkdGhHUSYwLjBlbUYnLyUmZGVwdGhHRl9zLyUqbGluZWJyZWFrR1EobmV3bGluZUYnLUYsNiVRI3BlRidGL0YyRjUtRiw2JVEoZGlzcGxheUYnRi9GMi1GUzYkLUYjNiotRiw2JVEkc2VxRidGL0YyLUZTNiQtRiM2K0ZXLUZTNiQtRiM2Li1GLDYlUSZFbGlzdEYnRi9GMi1GUzYmLUYjNiVGYXEvJStleGVjdXRhYmxlR0Y9RjlGOUZbcUZecUZaLUYsNiVRJmNvbG9yRidGL0YyRmpvLUYsNiVRJWJsdWVGJ0YvRjJGWi1GLDYlUSpudW1wb2ludHNGJ0YvRjJGam8tRmRwNiRRJDUwMEYnRjlGZHVGOUY5RlpGYXFGam9GZHEtRiw2I1EhRidGZHVGOUY5RlotRiw2JVEraW5zZXF1ZW5jZUYnRi9GMkZqby1GLDYlRjFGL0YyRmR1RjlGOUZeckZnckZqckZbdC1GUzYkLUYjNilGK0ZaRmhzLUYjNiZGWi1GIzYmLUYsNiVRJXZpZXdGJ0YvRjJGam8tRlM2Ji1GIzYsRl1wRmNwRmdwRmNwRlpGXXAtRmRwNiRRJDAuN0YnRjlGZ3BGW3JGOUY5RltxRl5xRjlGYnZGOUZidkZkdUY5RjktRjY2LVEiO0YnRjlGO0ZnbkZARkJGREZGRkhGaG5GTUZeckZkdUY5

<Text-field style="Heading 1" layout="Heading 1">Generalized sinc expansion on interval <Equation executable="false" style="2D Math" input-equation="" display="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">LUklbXJvd0c2Iy9JK21vZHVsZW5hbWVHNiJJLFR5cGVzZXR0aW5nR0koX3N5c2xpYkdGJzYpLUkobWZlbmNlZEdGJDYlLUYjNiwtSSNtb0dGJDYvUSomdW1pbnVzMDtGJy8lJXNpemVHUSMxOEYnLyUrZm9yZWdyb3VuZEdRKFswLDAsMF1GJy8lLG1hdGh2YXJpYW50R1Enbm9ybWFsRicvJSZmZW5jZUdRJmZhbHNlRicvJSpzZXBhcmF0b3JHRj8vJSlzdHJldGNoeUdGPy8lKnN5bW1ldHJpY0dGPy8lKGxhcmdlb3BHRj8vJS5tb3ZhYmxlbGltaXRzR0Y/LyUnYWNjZW50R0Y/LyUnbHNwYWNlR1EsMC4yMjIyMjIyZW1GJy8lJ3JzcGFjZUdGTi1GMTYwUSgmaW5maW47RidGNC8lJ2l0YWxpY0dRJXRydWVGJ0Y3L0Y7USdpdGFsaWNGJ0Y9RkBGQkZERkZGSEZKL0ZNUSYwLjBlbUYnL0ZQRlotRjE2MFEjLi5GJ0Y0RlRGN0ZXRj1GQEZCRkRGRkZIRkpGTEZlbkZRRjQvJSVib2xkR0ZWRjcvJTBmb250X3N0eWxlX25hbWVHUSpIZWFkaW5nfjFGJy9GO1ElYm9sZEYnLyUrZm9udHdlaWdodEdGX29GN0Y6RjRGaW5GN0Zbb0Zeb0Zgbw==</Equation></Text-field>

Functions for expansion:

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

Enter rolloff factor (m\342\210\210\342\204\225): m=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea23); end use;

If m=1 then the procedure returns sinc expansion (Whittaker-Shannon-Kotelnikov series expansion).

If m=2 or m=3 the expansions is not orthogonal.

Select function for expansion:

use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; 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

Reading of the selected parameters

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

List of the expansions evaluation

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

Animation of expansions

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

<Text-field style="Heading 1" layout="Heading 1">Sinc Wavelets expansion on interval <Equation executable="false" style="Heading 1" input-equation="" display="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">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</Equation></Text-field>

Functions for expansion:

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

Enter initial shift parameter: a=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea17); end use;

Enter initial scale parameter (d>0): d=use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. # a:=Do(%TextArea18); end use;

Select function for expansion:

use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; use DocumentTools in # Enter Maple commands to be executed when the specified # action is carried out on the component. # Use: # Do( %component_name ); # and # Do( %component_name = value ); # to set and get properties of the component. # You can also use arbitrary expressions # involving components, e.g.: # Do( %target = %input1 + 2*%input2 ); # Note the %-prefix to each component name. # See ?CustomizingComponents for more information. end use; 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

Reading of the selected parameters

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

List of the expansions evaluation

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

Animation of expansions

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