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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Representations through more general functions > Through Meijer G > Generalized cases involving Laguerre L





http://functions.wolfram.com/07.33.26.0033.01









  


  








Input Form





HypergeometricU[a, 1, z] LaguerreL[-a, -z] == ((Gamma[1 - a] Sin[a Pi])/(2 Pi^(3/2))) MeijerG[{{1 - a}, {a}}, {{0, 0, 1/2}, {0}}, z/2, 1/2]








Standard Form





Cell[BoxData[RowBox[List[RowBox[List[RowBox[List["HypergeometricU", "[", RowBox[List["a", ",", "1", ",", "z"]], "]"]], " ", RowBox[List["LaguerreL", "[", RowBox[List[RowBox[List["-", "a"]], ",", RowBox[List["-", "z"]]]], "]"]]]], "\[Equal]", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["1", "-", "a"]], "]"]], " ", RowBox[List["Sin", "[", RowBox[List["a", " ", "\[Pi]"]], "]"]]]], RowBox[List["2", " ", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]]], RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", "a"]], "}"]], ",", RowBox[List["{", "a", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["0", ",", "0", ",", FractionBox["1", "2"]]], "}"]], ",", RowBox[List["{", "0", "}"]]]], "}"]], ",", FractionBox["z", "2"], ",", FractionBox["1", "2"]]], "]"]]]]]]]]








MathML Form







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Rule Form





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





2007-05-02