orthopoly
U
Chebyshev polynomial of the second kind
Calling Sequence
Parameters
Description
Examples
U(n, x)
n
-
non-negative integer
x
algebraic expression
The U(n, x) function computes the nth Chebyshev polynomial of the second kind evaluated at x.
These polynomials are orthogonal on the interval −1,1 with respect to the weight function wx=−x2+1. They satisfy:
∫−11wtUm,tUn,tⅆt=0n≠mπ2n=m
Chebyshev polynomials of the second kind satisfy the following recurrence relation:
U0,x=1,
U1,x=2x,
Un,x=2xUn−1,x−Un−2,x,for n>1.
withorthopoly:
U2,x
4x2−1
U3,x
8x3−4x
U50,13
−40279025819534204641685717897987691852588770249
See Also
ChebyshevU
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