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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==infinity > For the function itself > Expansions in 1/(1-z)





http://functions.wolfram.com/07.13.06.0028.01









  


  








Input Form





GegenbauerC[\[Nu], z] == ((2^(1 - Abs[\[Nu]])/\[Nu]) Hypergeometric2F1[Abs[\[Nu]], 1/2 + Abs[\[Nu]], 1 + 2 Abs[\[Nu]], 2/(1 - z)])/(z - 1)^Abs[\[Nu]] + (2^Abs[\[Nu]]/\[Nu]) (z - 1)^Abs[\[Nu]] Sum[((Pochhammer[1/2 - Abs[\[Nu]], k] Pochhammer[-Abs[\[Nu]], k])/ (k! Pochhammer[1 - 2 Abs[\[Nu]], k])) (2/(1 - z))^k, {k, 0, Abs[\[Nu]] - 1/2}] /; Element[\[Nu] - 1/2, Integers]








Standard Form





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MathML Form







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</ci> <cn type='integer'> 0 </cn> <ci> z </ci> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <power /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <power /> <apply> <plus /> <ci> z </ci> <cn type='integer'> -1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <ci> Hypergeometric2F1 </ci> <apply> <abs /> <ci> &#957; </ci> </apply> <apply> <plus /> <apply> <abs /> <ci> &#957; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <abs /> <ci> &#957; </ci> </apply> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <abs /> <ci> &#957; 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Rule Form





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





2001-10-29