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BUILT-IN MATHEMATICA SYMBOL
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 
.
Gegenbauer polynomial:
renormalized Gegenbauer polynomial:
New in 1
