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Exp




Mathematica Notation

Traditional Notation









Elementary Functions > Exp[z] > Representations through more general functions > Through Meijer G > Generalized cases involving WhittakerM M





http://functions.wolfram.com/01.03.26.0260.01









  


  








Input Form





E^z WhittakerM[\[Nu], \[Mu], 2 z] - WhittakerM[-\[Nu], \[Mu], 2 z]/E^z == ((2^(1 - \[Nu]) Pi^(3/2) Gamma[1 + 2 \[Mu]])/Gamma[1/2 + \[Mu] - \[Nu]]) MeijerG[{{(1 + \[Nu])/2, (2 + \[Nu])/2}, {(1/4) (5 + 2 \[Mu])}}, {{(1/4) (3 + 2 \[Mu])}, {(1/4) (1 + 2 \[Mu]), (1/4) (5 + 2 \[Mu]), (1/4) (1 - 2 \[Mu]), (1/4) (3 - 2 \[Mu])}}, z, 1/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "z"], RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]", ",", "\[Mu]", ",", RowBox[List["2", "z"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z"]]], RowBox[List["WhittakerM", "[", RowBox[List[RowBox[List["-", "\[Nu]"]], ",", "\[Mu]", ",", RowBox[List["2", "z"]]]], "]"]]]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "]"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]]]]]]








MathML Form







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</ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> </list> </list> <list> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> 3 </cn> </apply> </apply> </list> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List[SuperscriptBox["\[ExponentialE]", "z_"], " ", RowBox[List["WhittakerM", "[", RowBox[List["\[Nu]_", ",", "\[Mu]_", ",", RowBox[List["2", " ", "z_"]]]], "]"]]]], "-", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", "z_"]]], " ", RowBox[List["WhittakerM", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", "\[Mu]_", ",", RowBox[List["2", " ", "z_"]]]], "]"]]]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List["1", "-", "\[Nu]"]]], " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]", "-", "\[Nu]"]], "]"]]]]]]]


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





2007-05-02