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variants of this functions
LaguerreL




Mathematica Notation

Traditional Notation









Hypergeometric Functions > LaguerreL[nu,z] > Representations through more general functions > Through Meijer G > Generalized cases involving exp and hypergeometric U





http://functions.wolfram.com/07.02.26.0027.01









  


  








Input Form





(HypergeometricU[1 + \[Nu], 1, z] LaguerreL[\[Nu], z])/E^z == (1/(2 Sqrt[Pi] Gamma[1 + \[Nu]])) MeijerG[{{-\[Nu]}, {1 + \[Nu]}}, {{0, 0, 1/2}, {0}}, 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["-", "z_"]]], " ", RowBox[List["HypergeometricU", "[", RowBox[List[RowBox[List["1", "+", "\[Nu]_"]], ",", "1", ",", "z_"]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["-", "\[Nu]"]], "}"]], ",", RowBox[List["{", RowBox[List["1", "+", "\[Nu]"]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", FractionBox["z", "2"], ",", FractionBox["1", "2"]]], "]"]], RowBox[List["2", " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]"]], "]"]]]]]]]]]


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





2007-05-02