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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 > Classical cases involving Bessel I





http://functions.wolfram.com/07.18.26.0120.01









  


  










Input Form





Hypergeometric0F1Regularized[b, z] BesselI[-b, 2 Sqrt[z]] == (1/Sqrt[Pi]) (Sin[b Pi]/(z^(b/2) Sqrt[Pi]) - 2^(-(1/2) + b) Pi MeijerG[{{(1 - b)/2, 1 - b/2}, {(1/4) (3 - 2 b)}}, {{1 - b/2}, {b/2, -(b/2), 1 - (3 b)/2, (1/4) (3 - 2 b)}}, 4 z])










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_", ",", "z_"]], "]"]], " ", RowBox[List["BesselI", "[", RowBox[List[RowBox[List["-", "b_"]], ",", RowBox[List["2", " ", SqrtBox["z_"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[FractionBox[RowBox[List[SuperscriptBox["z", RowBox[List["-", FractionBox["b", "2"]]]], " ", RowBox[List["Sin", "[", RowBox[List["b", " ", "\[Pi]"]], "]"]]]], SqrtBox["\[Pi]"]], "-", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "+", "b"]]], " ", "\[Pi]", " ", 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["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["b", "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["b", "2"], ",", RowBox[List["-", FractionBox["b", "2"]]], ",", RowBox[List["1", "-", FractionBox[RowBox[List["3", " ", "b"]], "2"]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["3", "-", RowBox[List["2", " ", "b"]]]], ")"]]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]]]], SqrtBox["\[Pi]"]]]]]]










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





2007-05-02