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BesselI




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselI[nu,z] > Representations through more general functions > Through Meijer G > Generalized cases involving 0F1





http://functions.wolfram.com/03.02.26.0146.01









  


  








Input Form





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


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





2007-05-02