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variants of this functions
ChebyshevU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > ChebyshevU[nu,z] > Summation > Infinite summation





http://functions.wolfram.com/07.05.23.0006.01









  


  








Input Form





Sum[(Pochhammer[\[Gamma], n]/(n + 1)!) ChebyshevU[n, z] w^n, {n, 0, Infinity}] == Hypergeometric2F1[\[Gamma]/2, (\[Gamma] + 1)/2, 3/2, ((z^2 - 1) w^2)/(1 - w z)^2]/(1 - w z)^\[Gamma] /; -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> <mi> &#947; </mi> <mo> ) </mo> </mrow> <mi> n </mi> </msub> <annotation encoding='Mathematica'> TagBox[SubscriptBox[RowBox[List[&quot;(&quot;, &quot;\[Gamma]&quot;, &quot;)&quot;]], &quot;n&quot;], Pochhammer] </annotation> </semantics> <mrow> <mrow> <mo> ( </mo> <mrow> <mi> n </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ! </mo> </mrow> </mfrac> <mo> &#8290; </mo> <mrow> <msub> <mi> U </mi> <mi> n </mi> </msub> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mi> n </mi> </msup> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mrow> <mo> - </mo> <mi> &#947; </mi> </mrow> </msup> <mo> &#8290; </mo> <semantics> <mrow> <mrow> <msub> <mo> &#8202; </mo> <mn> 2 </mn> </msub> <msub> <mi> F </mi> <mn> 1 </mn> </msub> </mrow> <mo> &#8289; </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mfrac> <mi> &#947; </mi> <mn> 2 </mn> </mfrac> <mo> , </mo> <mfrac> <mrow> <mi> &#947; </mi> <mo> + </mo> <mn> 1 </mn> </mrow> <mn> 2 </mn> </mfrac> </mrow> <mo> ; </mo> <mfrac> <mn> 3 </mn> <mn> 2 </mn> </mfrac> <mo> ; </mo> <mfrac> <mrow> <mrow> <mo> ( </mo> <mrow> <msup> <mi> z </mi> <mn> 2 </mn> </msup> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mi> w </mi> <mn> 2 </mn> </msup> </mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <mi> w </mi> <mo> &#8290; </mo> <mi> z </mi> </mrow> </mrow> <mo> ) </mo> </mrow> <mn> 2 </mn> </msup> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <annotation encoding='Mathematica'> TagBox[TagBox[RowBox[List[RowBox[List[SubscriptBox[&quot;\[InvisiblePrefixScriptBase]&quot;, FormBox[&quot;2&quot;, TraditionalForm]], SubscriptBox[&quot;F&quot;, FormBox[&quot;1&quot;, TraditionalForm]]]], &quot;\[InvisibleApplication]&quot;, RowBox[List[&quot;(&quot;, RowBox[List[TagBox[TagBox[RowBox[List[TagBox[FractionBox[&quot;\[Gamma]&quot;, &quot;2&quot;], Hypergeometric2F1, Rule[Editable, True]], &quot;,&quot;, TagBox[FractionBox[RowBox[List[&quot;\[Gamma]&quot;, &quot;+&quot;, &quot;1&quot;]], &quot;2&quot;], Hypergeometric2F1, Rule[Editable, True]]]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[TagBox[TagBox[FractionBox[&quot;3&quot;, &quot;2&quot;], Hypergeometric2F1, Rule[Editable, True]], InterpretTemplate[Function[List[SlotSequence[1]]]]], Hypergeometric2F1, Rule[Editable, False]], &quot;;&quot;, TagBox[FractionBox[RowBox[List[RowBox[List[&quot;(&quot;, RowBox[List[SuperscriptBox[&quot;z&quot;, &quot;2&quot;], &quot;-&quot;, &quot;1&quot;]], &quot;)&quot;]], &quot; 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Rule Form





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





2001-10-29