GegenbauerC

GegenbauerC[n,m,x]

gives the Gegenbauer polynomial .

GegenbauerC[n,x]

gives the renormalized form .

Details

  • 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 .

Examples

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Basic Examples  (2)

Compute the 10^(th) Gegenbauer polynomial:

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Compute the 10^(th) renormalized Gegenbauer polynomial:

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Plot :

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Scope  (6)

Generalizations & Extensions  (2)

Applications  (2)

Properties & Relations  (4)

Possible Issues  (1)

See Also

LegendreP  ChebyshevT  ChebyshevU  JacobiP

Tutorials

Introduced in 1996
(3.0)