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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Series representations > Generalized power series > Expansions at lambda==infinity





http://functions.wolfram.com/05.09.06.0049.01









  


  








Input Form





GegenbauerC[n, \[Lambda], z] \[Proportional] (((2 z)^n \[Lambda]^n)/n!) (1 + ((n - 1) n (2 z^2 - 1))/(4 z^2 \[Lambda]) + ((n - 2) (n - 1) n (3 n (1 - 2 z^2)^2 - (3 - 2 z^2)^2))/ (96 z^4 \[Lambda]^2) + \[Ellipsis]) /; (Abs[\[Lambda]] -> Infinity)








Standard Form





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MathML Form







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</ci> <ci> n </ci> </apply> <apply> <power /> <apply> <factorial /> <ci> n </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> <ci> n </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <ci> &#955; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <plus /> <ci> n </ci> <cn type='integer'> -2 </cn> </apply> <apply> <plus /> <ci> n </ci> <cn type='integer'> -1 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> n </ci> <apply> <power /> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <apply> <plus /> <cn type='integer'> 3 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <ci> n </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 96 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <ci> &#955; 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Rule Form





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





2007-05-02