numapprox
chebdeg
degree of a polynomial in Chebyshev form
Calling Sequence
Parameters
Description
Examples
chebdeg(p)
p
-
expression assumed to be a Chebyshev series
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.
withnumapprox:
Digits≔3:
a≔chebyshevsinx,x:
b≔chebyshevcosx,x:
c≔a+b
c≔0.880T1,x−0.0391T3,x+0.000500T5,x+0.765T0,x−0.230T2,x+0.00495T4,x
chebdegc
5
d≔a+cjTj,x+ckTk,x
d≔0.880T1,x−0.0391T3,x+0.000500T5,x+cjTj,x+ckTk,x
chebdegd
max5,j,k
assume5<k,k<j
e≔1.2y+cjTj,x+a+ckTk,x
e≔1.2y+cjTj~,x+0.880T1,x−0.0391T3,x+0.000500T5,x+ckTk~,x
chebdege
j~
See Also
numapprox[chebsort]
numapprox[chebyshev]
orthopoly[T]
Download Help Document