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BesselJ




Mathematica Notation

Traditional Notation









Bessel-Type Functions > BesselJ[nu,z] > Integral representations > Contour integral representations





http://functions.wolfram.com/03.01.07.0012.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["BesselJ", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox[RowBox[List["\[Pi]", " ", SuperscriptBox["z", "\[Nu]"], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "z"]], ")"]], RowBox[List["-", "\[Nu]"]]]]], RowBox[List["2", "\[Pi]", " ", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox["\[Nu]", "2"]]], "]"]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["\[Nu]", "+", "1"]], "2"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List["1", "+", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox[RowBox[List["1", "-", "\[Nu]"]], "2"], "-", "s"]], "]"]]]]], SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], ")"]], RowBox[List[RowBox[List["-", "2"]], "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]]]]








MathML Form







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Rule Form





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


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





2001-10-29