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GegenbauerC

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 (1-x^2)y^(′′)-(2m+1)xy^′+n(n+2m)y=0.
  • The Gegenbauer polynomials are orthogonal on the interval (-1,1) with weight function (1-x^2)^(m-1/2), 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[n, m, z] has a branch cut discontinuity in the complex z plane running from -∞ to -1.
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