numapprox - Maple Programming Help

Online Help

All Products    Maple    MapleSim


Home : Support : Online Help : Mathematics : Numerical Computations : Approximations : numapprox Package : numapprox/chebdeg

numapprox

  

chebdeg

  

degree of a polynomial in Chebyshev form

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

chebdeg(p)

Parameters

p

-

expression assumed to be a Chebyshev series

Description

• 

Given a polynomial p expressed as a Chebyshev series, determine the degree of the polynomial (i.e. the largest k such that Tk,x appears as a basis polynomial).

• 

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

• 

The input polynomial 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 (i.e. it is assumed to be a term of degree 0).

• 

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

Examples

withnumapprox:

Digits3:

achebyshevsinx,x:

bchebyshevcosx,x:

ca+b

c:=0.880T1,x0.0391T3,x+0.000500T5,x+0.765T0,x0.230T2,x+0.00495T4,x

(1)

chebdegc

5

(2)

da+cjTj,x+ckTk,x

d:=0.880T1,x0.0391T3,x+0.000500T5,x+cjTj,x+ckTk,x

(3)

chebdegd

max5,j,k

(4)

assume5<k&comma;k<j

e1.2y&plus;cjTj&comma;x&plus;a&plus;ckTk&comma;x

e:=1.2y&plus;cjTj~&comma;x&plus;0.880T1&comma;x0.0391T3&comma;x&plus;0.000500T5&comma;x&plus;ckTk~&comma;x

(5)

chebdege

j~

(6)

See Also

numapprox[chebsort]

numapprox[chebyshev]

orthopoly[T]

 


Download Help Document

Was this information helpful?



Please add your Comment (Optional)
E-mail Address (Optional)
What is ? This question helps us to combat spam