GegenbauerC

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

GegenbauerC[n, x] 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.

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

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

See Section 3.2.9.

See also: LegendreP, ChebyshevT, ChebyshevU.

New in Version 1.

Further Examples