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variants of this functions
GegenbauerC




Mathematica Notation

Traditional Notation









Hypergeometric Functions > GegenbauerC[nu,lambda,z] > Summation > Infinite summation





http://functions.wolfram.com/07.14.23.0006.01









  


  








Input Form





Sum[((Pochhammer[\[Gamma], n] Pochhammer[2 \[Lambda] - \[Gamma], n])/ (Pochhammer[2 \[Lambda], n] Pochhammer[\[Lambda] + 1/2, n])) GegenbauerC[n, \[Lambda], z] w^n, {n, 0, Infinity}] == Hypergeometric2F1[\[Gamma], 2 \[Lambda] - \[Gamma], \[Lambda] + 1/2, (1 - Sqrt[w^2 - 2 w z + 1] - w)/2] Hypergeometric2F1[\[Gamma], 2 \[Lambda] - \[Gamma], \[Lambda] + 1/2, (1 - Sqrt[w^2 - 2 w z + 1] + w)/ 2] /; -1 < z < 1 && Abs[w] < 1








Standard Form





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MathML Form







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</mo> <mrow> <mrow> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> &lt; </mo> <mi> z </mi> <mo> &lt; </mo> <mn> 1 </mn> </mrow> <mo> &#8743; </mo> <mrow> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> w </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> <mo> &lt; </mo> <mn> 1 </mn> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <sum /> <bvar> <ci> n </ci> </bvar> <lowlimit> <cn type='integer'> 0 </cn> </lowlimit> <uplimit> <infinity /> </uplimit> <apply> <times /> <apply> <times /> <apply> <ci> Pochhammer </ci> <ci> &#947; </ci> <ci> n </ci> </apply> <apply> <ci> Pochhammer </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#955; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#947; </ci> </apply> </apply> <ci> n </ci> </apply> <apply> <power /> <apply> <times /> <apply> <ci> Pochhammer </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#955; 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Rule Form





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





2001-10-29