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G

  

Gegenbauer (ultraspherical) polynomial

 

Calling Sequence

Parameters

Description

Examples

Calling Sequence

G(n, a, x)

Parameters

n

-

non-negative integer

a

-

rational number greater than  or nonrational algebraic expression

x

-

algebraic expression

Description

• 

The G(n, a, x) function computes the nth ultraspherical (Gegenbauer) polynomial with parameter a evaluated at x.

• 

These polynomials are orthogonal on the interval  with respect to the weight function . For  they satisfy:

• 

When , , and  for , where  is the nth Chebyshev polynomial of the first kind.

• 

The ultraspherical polynomials satisfy the following recurrence relation, for .

Examples

(1)

(2)

(3)

See Also

GAMMA

GegenbauerC

 


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