multiply two Chebyshev series - Maple Help

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numapprox[chebmult] - multiply two Chebyshev series

Calling Sequence

chebmult(p, q)

Parameters

p, q

-

two expressions assumed to be Chebyshev series

Description

• 

Given polynomials p and q expressed in a Chebyshev basis, form the product pq expressed in a Chebyshev basis.

• 

All Chebyshev basis polynomials Tk,x which appear must have the same second argument x (which can be any expression).

• 

The input polynomials must be in expanded form (i.e. a sum of products). Normally, each term in the sum contains one and only one Tk,x factor except that if there are terms in the sum containing no Tk,x factor then each such term t is interpreted to represent tT0,x provided that t and x have no variables in common.

• 

If no Tk,x factor appears in p or in q then the ordinary product pq is returned.

• 

The command with(numapprox,chebmult) allows the use of the abbreviated form of this command.

Examples

withnumapprox:

Digits:=3:

a:=chebyshevsinx,x

a:=0.880T1,x0.0391T3,x+0.000500T5,x

(1)

b:=chebyshevⅇx,x

b:=1.26T0,x+1.13T1,x+0.271T2,x+0.0443T3,x+0.00547T4,x+0.000543T5,x

(2)

chebmulta,b

0.496T0,x+1.22T1,x+0.494T2,x+0.0718T3,x0.00212T4,x0.00227T5,x0.000344T6,x0.0000390T7,x+5.10-7T8,x+0.00000137T9,x+1.3610-7T10,x

(3)

c:=c0T0,x+c1T1,x

c:=c0T0,x+c1T1,x

(4)

d:=d0T0,x+d1T1,x

d:=d0T0,x+d1T1,x

(5)

chebmultc,d

c0d0+12d1c1T0,x+c0d1+d0c1T1,x+12d1c1T2,x

(6)

chebmultTj,x,Tk,x

12Tk+j,x+12Tk+j,x

(7)

assume0<j&comma;j<k

chebmultc0&plus;cjTj&comma;x&comma;Tk&comma;x

12cjTk~j~&comma;x&plus;c0Tk~&comma;x&plus;12cjTj~&plus;k~&comma;x

(8)

assume5<j&comma;j<k

e:=a&plus;ckTk&comma;x

e:=0.880T1&comma;x0.0391T3&comma;x&plus;0.000500T5&comma;x&plus;ckTk~&comma;x

(9)

chebmulte&comma;Tj&comma;x

0.500ckTk~j~&comma;x&plus;0.000250Tj~5&comma;x0.0196Tj~3&comma;x&plus;0.440Tj~1&comma;x&plus;0.440T1&plus;j~&comma;x0.0196T3&plus;j~&comma;x&plus;0.000250T5&plus;j~&comma;x&plus;0.500ckTk~&plus;j~&comma;x

(10)

See Also

numapprox[chebsort], numapprox[chebyshev], orthopoly[T]


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