Chebyshev polynomial of the second kind - Maple Help

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orthopoly[U] - Chebyshev polynomial of the second kind

Calling Sequence

U(n, x)

Parameters

n

-

non-negative integer

x

-

algebraic expression

Description

• 

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=0nmπ2n=m

• 

Chebyshev polynomials of the second kind satisfy the following recurrence relation:

U0,x=1,

U1,x=2x,

Un,x=2xUn1,xUn2,x,for n>1.

Examples

withorthopoly:

U2,x

4x21

(1)

U3,x

8x34x

(2)

U50,13

40279025819534204641685717897987691852588770249

(3)

See Also

ChebyshevU


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