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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,z] > Series representations > Generalized power series > Expansions at z==-1 > For the function itself > General case





http://functions.wolfram.com/07.13.06.0056.01









  


  










Input Form





GegenbauerC[\[Nu], z] == Subscript[F, Infinity][z, \[Nu]] /; Subscript[F, m][z, \[Nu]] == (2/\[Nu]) Cos[\[Nu] Pi] Sum[((Pochhammer[-\[Nu], k] Pochhammer[\[Nu], k])/(Pochhammer[1/2, k] k!)) ((z + 1)/2)^k, {k, 0, m}] + 2 Sqrt[2] Sin[\[Nu] Pi] Sqrt[1 + z] Sum[((Pochhammer[1/2 - \[Nu], k] Pochhammer[1/2 + \[Nu], k])/ (Pochhammer[3/2, k] k!)) ((z + 1)/2)^k, {k, 0, m}] == GegenbauerC[\[Nu], z] - ((Cos[Pi \[Nu]] Pochhammer[-\[Nu], 1 + m] Pochhammer[\[Nu] + 1, m])/(2^m ((1 + m)! Pochhammer[1/2, 1 + m]))) (1 + z)^(1 + m) HypergeometricPFQ[{1, 1 + m - \[Nu], 1 + m + \[Nu]}, {3/2 + m, 2 + m}, (1 + z)/2] - ((2^(1/2 - m) Sin[Pi \[Nu]] Pochhammer[1/2 - \[Nu], 1 + m] Pochhammer[1/2 + \[Nu], 1 + m])/((1 + m)! Pochhammer[3/2, 1 + m])) (1 + z)^(3/2 + m) HypergeometricPFQ[{1, 3/2 + m - \[Nu], 3/2 + m + \[Nu]}, {2 + m, 5/2 + m}, (1 + z)/2] && Element[m, Integers] && m >= 0










Standard Form





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MathML Form







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Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02