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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 Laguerre L





http://functions.wolfram.com/07.44.26.0093.01









  


  








Input Form





(LaguerreL[\[Lambda], -1 - 2 \[Lambda], z] WhittakerM[0, \[Mu], z])/ E^(z/2) == ((2^(1/2 + \[Lambda] + \[Mu]) z^(1/2 + \[Mu]) Gamma[1 + \[Mu]])/ Gamma[1 + \[Lambda]]) MeijerG[{{(1/4) (3 + 2 \[Lambda] - 2 \[Mu]), (1/4) (1 + 2 \[Lambda] - 2 \[Mu])}, {}}, {{0}, {1/2 + \[Lambda] - \[Mu], 1/2 + \[Lambda], -\[Mu]}}, (I z)/2, 1/2]








Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[SuperscriptBox["\[ExponentialE]", RowBox[List["-", FractionBox["z_", "2"]]]], " ", RowBox[List["LaguerreL", "[", RowBox[List["\[Lambda]_", ",", RowBox[List[RowBox[List["-", "1"]], "-", RowBox[List["2", " ", "\[Lambda]_"]]]], ",", "z_"]], "]"]], " ", RowBox[List["WhittakerM", "[", RowBox[List["0", ",", "\[Mu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "2"], "+", "\[Lambda]", "+", "\[Mu]"]]], " ", SuperscriptBox["z", RowBox[List[FractionBox["1", "2"], "+", "\[Mu]"]]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Mu]"]], "]"]]]], ")"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "+", RowBox[List["2", " ", "\[Lambda]"]], "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "+", RowBox[List["2", " ", "\[Lambda]"]], "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "+", "\[Lambda]", "-", "\[Mu]"]], ",", RowBox[List[FractionBox["1", "2"], "+", "\[Lambda]"]], ",", RowBox[List["-", "\[Mu]"]]]], "}"]]]], "}"]], ",", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], ",", FractionBox["1", "2"]]], "]"]]]], RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Lambda]"]], "]"]]]]]]]


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





2007-05-02