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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/03.02.26.0034.01









  


  










Input Form





BesselI[\[Nu], z] Hypergeometric0F1Regularized[1 - \[Nu], -(z^2/4)] == Sqrt[Pi] 2^(\[Nu]/2) MeijerG[{{}, {(2 + 3 \[Nu])/4}}, {{\[Nu]/4, (\[Nu] + 2)/4}, {-(\[Nu]/4), (3 \[Nu])/4, (2 + 3 \[Nu])/4}}, z^4/64] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, Pi/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["Hypergeometric0F1Regularized", "[", RowBox[List[RowBox[List["1", "-", "\[Nu]_"]], ",", RowBox[List["-", FractionBox[SuperscriptBox["z_", "2"], "4"]]]]], "]"]]]], "]"]], "\[RuleDelayed]", RowBox[List[RowBox[List[SqrtBox["\[Pi]"], " ", SuperscriptBox["2", RowBox[List["\[Nu]", "/", "2"]]], " ", RowBox[List["MeijerG", "[", RowBox[List[RowBox[List["{", RowBox[List[RowBox[List["{", "}"]], ",", RowBox[List["{", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", "\[Nu]"]]]], ")"]]]], "}"]]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["{", RowBox[List[FractionBox["\[Nu]", "4"], ",", FractionBox[RowBox[List["\[Nu]", "+", "2"]], "4"]]], "}"]], ",", RowBox[List["{", RowBox[List[RowBox[List["-", FractionBox["\[Nu]", "4"]]], ",", FractionBox[RowBox[List["3", " ", "\[Nu]"]], "4"], ",", RowBox[List[FractionBox["1", "4"], " ", RowBox[List["(", RowBox[List["2", "+", RowBox[List["3", " ", "\[Nu]"]]]], ")"]]]]]], "}"]]]], "}"]], ",", FractionBox[SuperscriptBox["z", "4"], "64"]]], "]"]]]], "/;", RowBox[List[RowBox[List["-", FractionBox["\[Pi]", "2"]]], "<", RowBox[List["Arg", "[", "z", "]"]], "\[LessEqual]", FractionBox["\[Pi]", "2"]]]]]]]]]










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





2001-10-29





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