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BesselJ




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.01.26.0170.01









  


  








Input Form





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


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





2007-05-02