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variants of this functions
GegenbauerC






Mathematica Notation

Traditional Notation









Polynomials > GegenbauerC[n,lambda,z] > Representations through more general functions > Through Meijer G > Classical cases involving unit step theta





http://functions.wolfram.com/05.09.26.0025.01









  


  










Input Form





UnitStep[1 - Abs[z]] (1 - z)^(-\[Lambda] - n/2) GegenbauerC[n, \[Lambda], (2 - z)/(2 Sqrt[1 - z])] == (((-1)^n Gamma[1 - \[Lambda]])/n!) MeijerG[{{}, {1 - 2 \[Lambda] - n, 1 - \[Lambda]}}, {{0, 1 - 2 \[Lambda]}, {}}, z]










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> <semantics> <mi> &#952; </mi> <annotation-xml encoding='MathML-Content'> <ci> UnitStep </ci> </annotation-xml> </semantics> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mrow> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[LeftBracketingBar]&quot; </annotation> </semantics> <mi> z </mi> <semantics> <mo> &#10072; </mo> <annotation encoding='Mathematica'> &quot;\[RightBracketingBar]&quot; </annotation> </semantics> </mrow> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> n </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> - </mo> <mi> &#955; </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <msubsup> <mi> C </mi> <mi> n </mi> <mi> &#955; </mi> </msubsup> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> z </mi> </mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <msqrt> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> z </mi> </mrow> </msqrt> </mrow> </mfrac> <mo> ) </mo> </mrow> </mrow> </mrow> <mo> &#10869; </mo> <mrow> <mfrac> <mrow> <msup> <mrow> <mo> ( </mo> <mrow> <mo> - </mo> <mn> 1 </mn> </mrow> <mo> ) </mo> </mrow> <mi> n </mi> </msup> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8290; </mo> <mrow> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mi> &#955; </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <mrow> <mi> n </mi> <mo> ! 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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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