orthopoly
T
Chebyshev polynomial (of the first kind)
Calling Sequence
Parameters
Description
Examples
T(n, x)
n
-
non-negative integer
x
algebraic expression
The T(n, x) function computes the nth Chebyshev polynomial of the first kind evaluated at x.
These polynomials are orthogonal on the interval (−1,1) with respect to the weight function wx=1−x2+1. They satisfy:
∫−11wtTm,tTn,tⅆt=0n≠mπn=mandm=0π2n=mandm≠0
Chebyshev polynomials of the first kind satisfy the following recurrence relation:
T0,x=1,
T1,x=x,
Tn,x=2xTn−1,x−Tn−2,x,for n > 1.
withorthopoly:
T2,x
2x2−1
T3,x
4x3−3x
T50,13
203160711589551869872313717897987691852588770249
See Also
ChebyshevT
LambertW
numapprox[chebyshev]
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