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BesselI




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.02.26.0117.01









  


  








Input Form





BesselI[\[Nu], 2 Sqrt[z]] Hypergeometric0F1Regularized[-1 - \[Nu], z] == (2^(-(3/2) - \[Nu])/Pi) ((-Pi^(3/2)) MeijerG[{{(2 + \[Nu])/2, (3 + \[Nu])/2}, {(1/4) (5 + 2 \[Nu])}}, {{(4 + \[Nu])/2}, {-(\[Nu]/2), \[Nu]/2, 2 + (3 \[Nu])/2, (1/4) (5 + 2 \[Nu])}}, 4 z] + 2^(3/2 + \[Nu]) z^(\[Nu]/2) (1 + \[Nu]) 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["BesselI", "[", RowBox[List["\[Nu]_", ",", RowBox[List["2", " ", SqrtBox["z_"]]]]], "]"]], " ", RowBox[List["Hypergeometric0F1Regularized", "[", RowBox[List[RowBox[List[RowBox[List["-", "1"]], "-", "\[Nu]_"]], ",", "z_"]], "]"]]]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", FractionBox["3", "2"]]], "-", "\[Nu]"]]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox[RowBox[List["2", "+", "\[Nu]"]], "2"], ",", FractionBox[RowBox[List["3", "+", "\[Nu]"]], "2"]]], "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", FractionBox[RowBox[List["4", "+", "\[Nu]"]], "2"], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "2"]]], ",", FractionBox["\[Nu]", "2"], ",", RowBox[List["2", "+", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "2"]]], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["5", "+", RowBox[List["2", " ", "\[Nu]"]]]], ")"]]]]]], "}"]]]], "}"]], ",", RowBox[List["4", " ", "z"]]]], "]"]]]], "+", RowBox[List[SuperscriptBox["2", RowBox[List[FractionBox["3", "2"], "+", "\[Nu]"]]], " ", SuperscriptBox["z", RowBox[List["\[Nu]", "/", "2"]]], " ", RowBox[List["(", RowBox[List["1", "+", "\[Nu]"]], ")"]], " ", RowBox[List["Sin", "[", RowBox[List["\[Pi]", " ", "\[Nu]"]], "]"]]]]]], ")"]]]], "\[Pi]"]]]]]


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





2007-05-02