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WhittakerM






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Representations through more general functions > Through Meijer G > Generalized cases involving exp and hypergeometric U





http://functions.wolfram.com/07.44.26.0081.01









  


  










Input Form





(HypergeometricU[1/2 + \[Mu] - \[Nu], 1 + 2 \[Mu], z] WhittakerM[\[Nu], \[Mu], -z])/E^(z/2) == ((2^(-1 - 2 \[Mu]) (-z)^(1/2 + \[Mu]) Gamma[1 + 2 \[Mu]])/ (Sqrt[Pi] Gamma[1/2 + \[Mu] - \[Nu]])) MeijerG[{{1/2 - \[Mu] + \[Nu]}, {1/2 - \[Mu] - \[Nu]}}, {{0, 1/2 - \[Mu], -\[Mu]}, {-2 \[Mu]}}, z/2, 1/2]










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> <msup> <mi> &#8519; </mi> <mrow> <mo> - </mo> <mfrac> <mi> z </mi> <mn> 2 </mn> </mfrac> </mrow> </msup> <mo> &#8290; </mo> <mrow> <semantics> <mi> U </mi> <annotation encoding='Mathematica'> TagBox[&quot;U&quot;, HypergeometricU] </annotation> </semantics> <mo> ( </mo> <mrow> <mrow> <mi> &#956; </mi> <mo> - </mo> <mi> &#957; </mi> <mo> + </mo> <mfrac> <mn> 1 </mn> <mn> 2 </mn> </mfrac> </mrow> <mo> , </mo> <mrow> <mrow> <mn> 2 </mn> <mo> &#8290; </mo> <mi> &#956; </mi> </mrow> <mo> + </mo> <mn> 1 </mn> </mrow> <mo> , </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <msub> <semantics> <mi> M </mi> <annotation encoding='Mathematica'> TagBox[&quot;M&quot;, WhittakerM] </annotation> </semantics> <mrow> <mi> &#957; </mi> <mo> , </mo> <mi> &#956; </mi> </mrow> </msub> <mo> ( </mo> <mrow> <mo> - </mo> <mi> z </mi> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> &#63449; 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Rule Form





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





2007-05-02