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variants of this functions
Hypergeometric0F1Regularized




Mathematica Notation

Traditional Notation









Hypergeometric Functions > Hypergeometric0F1Regularized[b,z] > Representations through more general functions > Through Meijer G > Generalized cases involving Bessel Y





http://functions.wolfram.com/07.18.26.0199.01









  


  








Input Form





Hypergeometric0F1Regularized[b, -(z^2/4)] BesselY[-b, z] == -((2^b Cos[b Pi])/(z^b Pi)) + (2^(-1 + b)/Sqrt[Pi]) MeijerG[{{(1 - b)/2, 1 - b/2}, {(1 + b)/2}}, {{1 - b/2, b/2}, {1 - (3 b)/2, -(b/2), (1 + b)/2}}, z, 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[RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List["b_", ",", RowBox[List["-", FractionBox[SuperscriptBox["z_", "2"], "4"]]]]], "]"]], " ", RowBox[List["BesselY", "[", RowBox[List[RowBox[List["-", "b_"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List["-", FractionBox[RowBox[List[SuperscriptBox["2", "b"], " ", SuperscriptBox["z", RowBox[List["-", "b"]]], " ", RowBox[List["Cos", "[", RowBox[List["b", " ", "\[Pi]"]], "]"]]]], "\[Pi]"]]], "+", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "b"]], "2"], ",", RowBox[List["1", "-", FractionBox["b", "2"]]]]], "}"]], ",", RowBox[List["{", FractionBox[RowBox[List["1", "+", "b"]], "2"], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox["b", "2"]]], ",", FractionBox["b", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "b"]], "2"]]], ",", RowBox[List["-", FractionBox["b", "2"]]], ",", FractionBox[RowBox[List["1", "+", "b"]], "2"]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], SqrtBox["\[Pi]"]]]]]]]]


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





2007-05-02