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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 exp and 1F~1





http://functions.wolfram.com/07.44.26.0035.01









  


  










Input Form





E^(z/2) Hypergeometric1F1Regularized[c, 2 c, -z] WhittakerM[0, \[Mu], z] == ((2^(1/2 - c + \[Mu]) Pi z^(1/2 + \[Mu]) Gamma[1 + \[Mu]])/Gamma[c]) MeijerG[{{(1/4) (3 - 2 c - 2 \[Mu]), (1/4) (1 - 2 c - 2 \[Mu])}, {1/2}}, {{0}, {1/2 - c - \[Mu], 1/2 - c, -\[Mu], 1/2}}, z^2/4]










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]", FractionBox["z_", "2"]], " ", RowBox[List["Hypergeometric1F1Regularized", "[", RowBox[List["c_", ",", RowBox[List["2", " ", "c_"]], ",", RowBox[List["-", "z_"]]]], "]"]], " ", RowBox[List["WhittakerM", "[", RowBox[List["0", ",", "\[Mu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["1", "2"], "-", "c", "+", "\[Mu]"]]], " ", "\[Pi]", " ", 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", " ", "c"]], "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["1", "-", RowBox[List["2", " ", "c"]], "-", RowBox[List["2", " ", "\[Mu]"]]]], ")"]]]]]], "}"]], ",", RowBox[List["{", FractionBox["1", "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", "0", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List[FractionBox["1", "2"], "-", "c", "-", "\[Mu]"]], ",", RowBox[List[FractionBox["1", "2"], "-", "c"]], ",", RowBox[List["-", "\[Mu]"]], ",", FractionBox["1", "2"]]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "2"], "4"]]], "]"]]]], RowBox[List["Gamma", "[", "c", "]"]]]]]]]










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





2007-05-02