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WhittakerM






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Representations through more general functions > Through Meijer G > Classical cases involving cosh





http://functions.wolfram.com/07.44.26.0012.01









  


  










Input Form





Cosh[z/2] WhittakerM[\[Nu], \[Mu], z] == ((Pi Gamma[1 + 2 \[Mu]])/(2 Gamma[1/2 + \[Mu] - \[Nu]])) MeijerG[{{1 + \[Nu]}, {1 + \[Mu]}}, {{1/2 + \[Mu]}, {1/2 - \[Mu], 1 + \[Mu]}}, z] + (Gamma[1 + 2 \[Mu]]/(2 Gamma[1/2 + \[Mu] + \[Nu]])) MeijerG[{{1 - \[Nu]}, {}}, {{1/2 + \[Mu]}, {1/2 - \[Mu]}}, z]










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <plus /> <ci> &#956; </ci> <cn type='integer'> 1 </cn> </apply> </list> </list> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> MeijerG </ci> <list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </list> <list /> </list> <list> <list> <apply> <plus /> <ci> &#956; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> <list> <apply> <plus /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> </apply> </list> </list> <ci> z </ci> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Cosh", "[", FractionBox["z_", "2"], "]"]], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List["\[Pi]", " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "+", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "\[Mu]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", "\[Mu]"]], ",", RowBox[List["1", "+", "\[Mu]"]]]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "]"]]]]], "+", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "2"], "-", "\[Mu]"]], "}"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["2", " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "+", "\[Nu]"]], "]"]]]]]]]]]]]










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





2007-05-02