orthopoly
G
Gegenbauer (ultraspherical) polynomial
Calling Sequence
Parameters
Description
Examples
G(n, a, x)
n
-
non-negative integer
a
rational number greater than or nonrational algebraic expression
x
algebraic expression
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 .
See Also
GAMMA
GegenbauerC
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