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WhittakerW




Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerW[nu,mu,z] > Representations through more general functions > Through hypergeometric functions > Involving 1F1





http://functions.wolfram.com/07.45.26.0001.01









  


  








Input Form





WhittakerW[\[Nu], \[Mu], z] == (z^(1/2 + \[Mu]) ((Gamma[2 \[Mu]]/(z^(2 \[Mu]) Gamma[1/2 + \[Mu] - \[Nu]])) HypergeometricPFQ[{1/2 - \[Mu] - \[Nu]}, {1 - 2 \[Mu]}, z] + (Gamma[-2 \[Mu]]/Gamma[1/2 - \[Mu] - \[Nu]]) HypergeometricPFQ[ {1/2 + \[Mu] - \[Nu]}, {1 + 2 \[Mu]}, z]))/E^(z/2) /; !Element[2 \[Mu], Integers]








Standard Form





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MathML Form







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</ci> <ci> &#956; </ci> <ci> z </ci> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#956; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <apply> <plus /> <apply> <times /> <apply> <times /> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -2 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> <list> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> </apply> </apply> </list> <ci> z </ci> </apply> </apply> <apply> <times /> <apply> <times /> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -2 </cn> <ci> &#956; </ci> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#956; </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <plus /> <ci> &#956; </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </list> <list> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["WhittakerW", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z", "2"]]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["(", RowBox[List[FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["z", RowBox[List[RowBox[List["-", "2"]], " ", "\[Mu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["2", " ", "\[Mu]"]], "]"]]]], ")"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], "-", "\[Mu]", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "-", RowBox[List["2", " ", "\[Mu]"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "]"]]], "+", FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "2"]], " ", "\[Mu]"]], "]"]], " ", RowBox[List["HypergeometricPFQ", "[", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "}"]], ",", "z"]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "\[Mu]", "-", "\[Nu]"]], "]"]]]]], ")"]]]], "/;", RowBox[List["!", RowBox[List[RowBox[List["2", " ", "\[Mu]"]], "\[Element]", "Integers"]]]]]]]]]]


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





2007-05-02