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SphericalHarmonicYChebyshevT

GegenbauerC

FilledSmallSquareGegenbauerC[n, m, x] gives the Gegenbauer polynomial .

FilledSmallSquareGegenbauerC[n, x] gives the renormalized form .

FilledSmallSquare Mathematical function (see Section A.3.10).

FilledSmallSquare Explicit polynomials are given for integer n and for any m.

FilledSmallSquare satisfies the differential equation .

FilledSmallSquare The Gegenbauer polynomials are orthogonal on the interval with weight function , corresponding to integration over a unit hypersphere.

FilledSmallSquareGegenbauerC[n, 0, x] is always zero.

FilledSmallSquareGegenbauerC[n, m, z] has a branch cut discontinuity in the complex z plane running from to .

FilledSmallSquare See The Mathematica Book: Section 3.2.9.

FilledSmallSquare See also: LegendreP, ChebyshevT, ChebyshevU.

Further Examples

SphericalHarmonicYChebyshevT