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variants of this functions
Hypergeometric0F1






Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1[b,z] > Representations through more general functions > Through Meijer G > Generalized cases involving Bessel Y





http://functions.wolfram.com/07.17.26.0191.01









  


  










Input Form





Hypergeometric0F1[b, z^2/4] BesselY[-1 + b, z] == (-2^((1 - b)/2)) Sqrt[Pi] Gamma[b] MeijerG[{{}, {1 - b/4, (2 - b)/4}}, {{(3 - b)/4, (1 - b)/4, (b - 1)/4}, {1 - b/4, (2 - b)/4, (3 - 3 b)/4}}, z/(2 Sqrt[2]), 1/4]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List[RowBox[List["Hypergeometric0F1", "[", RowBox[List["b_", ",", FractionBox[SuperscriptBox["z_", "2"], "4"]]], "]"]], " ", RowBox[List["BesselY", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "+", "b_"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", SuperscriptBox["2", FractionBox[RowBox[List["1", "-", "b"]], "2"]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["Gamma", "[", "b", "]"]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["b", "4"]]], ",", FractionBox[RowBox[List["2", "-", "b"]], "4"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["3", "-", "b"]], "4"], ",", FractionBox[RowBox[List["1", "-", "b"]], "4"], ",", FractionBox[RowBox[List["b", "-", "1"]], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["b", "4"]]], ",", FractionBox[RowBox[List["2", "-", "b"]], "4"], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["3", " ", "b"]]]], ")"]]]]]], "}"]]]], "}"]], ",", FractionBox["z", RowBox[List["2", " ", SqrtBox["2"]]]], ",", FractionBox["1", "4"]]], "]"]]]]]]]]










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





2007-05-02