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variants of this functions
JacobiP






Mathematica Notation

Traditional Notation









Hypergeometric Functions > JacobiP[nu,a,b,z] > Summation > Infinite summation





http://functions.wolfram.com/07.15.23.0004.01









  


  










Input Form





Sum[((Pochhammer[a + b + 1, n] JacobiP[n, a, b, z])/Pochhammer[b + 1, n]) w^n, {n, 0, Infinity}] == (1 + w)^(-a - b - 1) Hypergeometric2F1[(a + b + 1)/2, (a + b)/2 + 1, b + 1, (2 (z + 1) w)/(1 + w)^2] /; -1 < z < 1 && Abs[w] < 1










Standard Form





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MathML Form







<math xmlns='http://www.w3.org/1998/Math/MathML' mathematica:form='TraditionalForm' xmlns:mathematica='http://www.wolfram.com/XML/'> <semantics> <mrow> <mrow> <mrow> <munderover> <mo> &#8721; </mo> <mrow> <mi> n </mi> <mo> = </mo> <mn> 0 </mn> </mrow> <mi> &#8734; </mi> </munderover> <mrow> <mfrac> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> a </mi> <mo> + </mo> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;a&quot;, &quot;+&quot;, &quot;b&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> <semantics> <msub> <mrow> <mo> ( </mo> <mrow> <mi> b </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, RowBox[List[&quot;b&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> </mfrac> <mo> &#8290; 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Rule Form





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





2001-10-29





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