BesselI[\[Nu], z] == ((2^(-\[Nu] - 1) z^\[Nu])/I) ContourIntegral[Gamma[s]/(Gamma[1/2 + s] Gamma[1/2 - s] Gamma[1 + \[Nu] - s])/(z^2/4)^s, \[ScriptCapitalL]["s"]]

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Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["BesselI", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["2", RowBox[List[RowBox[List["-", "\[Nu]"]], "-", "1"]]], " ", SuperscriptBox["z", "\[Nu]"]]], ")"]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", "s", "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[SuperscriptBox["z", "2"], "4"], ")"]], RowBox[List["-", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "+", "\[Nu]", "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], "\[ImaginaryI]"]]]]]

2001-10-29