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GegenbauerC

Usage

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


Notes

• 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 also: LegendreP, ChebyshevT, ChebyshevU.
• New in Version 1.


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