This is documentation for Mathematica 5, which was
based on an earlier version of the Wolfram Language.
View current documentation (Version 11.2)

Documentation / Mathematica / Built-in Functions / Mathematical Functions / Orthogonal Polynomials /


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

FilledSmallSquare GegenbauerC[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.

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

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

FilledSmallSquare See Section 3.2.9.

FilledSmallSquare See also: LegendreP, ChebyshevT, ChebyshevU.

FilledSmallSquare New in Version 1.

Further Examples