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BesselJ




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselJ[nu,z] > Representations through more general functions > Through Meijer G > Classical cases involving 0F~1





http://functions.wolfram.com/03.01.26.0139.01









  


  








Input Form





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








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["BesselJ", "[", RowBox[List["\[Nu]_", ",", RowBox[List["2", " ", SqrtBox["z_"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List[RowBox[List["-", "\[Nu]_"]], ",", RowBox[List["-", "z_"]]]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["2", RowBox[List["-", "\[Nu]"]]]]], " ", SqrtBox["\[Pi]"], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["1", "+", "\[Nu]"]], "2"], ",", RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List["-", FractionBox["\[Nu]", "2"]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["1", "+", FractionBox["\[Nu]", "2"]]], ",", RowBox[List["-", FractionBox["\[Nu]", "2"]]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"], ",", RowBox[List["1", "+", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]], "-", RowBox[List["2", " ", SuperscriptBox["z", RowBox[List["\[Nu]", "/", "2"]]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]], RowBox[List["2", " ", "\[Pi]"]]]]]]]


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





2007-05-02