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

GegenbauerC[n, x]
gives the renormalized form .


  • Mathematical function, suitable for both symbolic and numerical manipulation.
  • 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.
  • For certain special arguments, GegenbauerC automatically evaluates to exact values.
  • GegenbauerC can be evaluated to arbitrary numerical precision.
  • GegenbauerC automatically threads over lists.
  • GegenbauerC[n, 0, x] is always zero.
  • GegenbauerC[n, m, z] has a branch cut discontinuity in the complex z plane running from to .
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