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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 J





http://functions.wolfram.com/07.17.26.0178.01









  


  










Input Form





Hypergeometric0F1[b, -(z^2/4)] BesselJ[b - 1, z] == (Gamma[b]/Sqrt[Pi]) 2^(-1 + b) MeijerG[{{1 - b/2}, {}}, {{(b - 1)/2}, {(1 - b)/2, (3/2) (1 - b)}}, 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["Hypergeometric0F1", "[", RowBox[List["b_", ",", RowBox[List["-", FractionBox[SuperscriptBox["z_", "2"], "4"]]]]], "]"]], " ", RowBox[List["BesselJ", "[", RowBox[List[RowBox[List["b_", "-", "1"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["Gamma", "[", "b", "]"]], " ", SuperscriptBox["2", RowBox[List[RowBox[List["-", "1"]], "+", "b"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List["1", "-", FractionBox["b", "2"]]], "}"]], ",", RowBox[List["{", "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["b", "-", "1"]], "2"], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "-", "b"]], "2"], ",", FractionBox[RowBox[List["3", " ", RowBox[List["(", RowBox[List["1", "-", "b"]], ")"]]]], "2"]]], "}"]]]], "}"]], ",", "z", ",", FractionBox["1", "2"]]], "]"]]]], SqrtBox["\[Pi]"]]]]]]










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





2007-05-02





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