] gives the Gegenbauer polynomial .
] gives the renormalized form .
Mathematical function (see Section A.3.10).
Explicit polynomials are given for integer n and for any m.
satisfies the differential equation .
The Gegenbauer polynomials are orthogonal on the interval with weight function , corresponding to integration over a unit hypersphere.
] is always zero.
] has a branch cut discontinuity in the complex z plane running from to .
See the Mathematica book: Section 3.2.9.
See also: LegendreP, ChebyshevT, ChebyshevU.
Here are the first ten GegenbauerC polynomials.
The Gegenbauer polynomials are pairwise orthogonal with respect to the appropriate weight function.
This is the derivative.
This is the indefinite integral.
This verifies the defining differential equation for n = 2 and m = 3.
This is a series expansion around .
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