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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 z==1 > For the function itself





http://functions.wolfram.com/05.09.06.0031.01









  


  










Input Form





GegenbauerC[n, \[Lambda], z] \[Proportional] (Pochhammer[2 \[Lambda], n]/n!) (1 + ((n (n + 2 \[Lambda]))/(1 + 2 \[Lambda])) (z - 1) + (((-1 + n) n (n + 2 \[Lambda]) (1 + n + 2 \[Lambda]))/ (2 (1 + 2 \[Lambda]) (3 + 2 \[Lambda]))) (z - 1)^2 + \[Ellipsis]) /; (z -> 1) && !(Element[-\[Lambda] - 1/2, Integers] && -\[Lambda] - 1/2 >= 0)










Standard Form





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MathML Form







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</mo> <mi> &#955; </mi> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mi> z </mi> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> + </mo> <mrow> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> + </mo> <mi> n </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mi> n </mi> <mo> &#8290; </mo> <mtext> </mtext> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mi> n </mi> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#955; </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 3 </mn> <mo> + </mo> <mrow> <mn> 2 </mn> <mo> &#8290; 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Rule Form





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





2007-05-02





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