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SphericalBesselJ






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.21.07.0012.01









  


  










Input Form





SphericalBesselJ[\[Nu], z] == (1/(2 Pi I)) ((Pi^(3/2) (I z)^(-(1/2) - \[Nu]) z^\[Nu])/Sqrt[2]) ContourIntegral[Gamma[1/4 + \[Nu]/2 + s]/(Gamma[3/4 + \[Nu]/2 + s] Gamma[1/4 - \[Nu]/2 - s] Gamma[5/4 + \[Nu]/2 - s])/((I z)/2)^(2 s), \[ScriptCapitalL]["s"]]










Standard Form





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MathML Form







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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["SphericalBesselJ", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", FractionBox[RowBox[List[RowBox[List["(", RowBox[List[SuperscriptBox["\[Pi]", RowBox[List["3", "/", "2"]]], " ", SuperscriptBox[RowBox[List["(", RowBox[List["\[ImaginaryI]", " ", "z"]], ")"]], RowBox[List[RowBox[List["-", FractionBox["1", "2"]]], "-", "\[Nu]"]]], " ", SuperscriptBox["z", "\[Nu]"]]], ")"]], " ", RowBox[List["ContourIntegral", "[", RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "4"], "+", FractionBox["\[Nu]", "2"], "+", "s"]], "]"]], " ", SuperscriptBox[RowBox[List["(", FractionBox[RowBox[List["\[ImaginaryI]", " ", "z"]], "2"], ")"]], RowBox[List[RowBox[List["-", "2"]], " ", "s"]]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["3", "4"], "+", FractionBox["\[Nu]", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "4"], "-", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[FractionBox["5", "4"], "+", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]]]], RowBox[List[RowBox[List["(", RowBox[List["2", " ", "\[Pi]", " ", "\[ImaginaryI]"]], ")"]], " ", SqrtBox["2"]]]]]]]]










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





2007-05-02





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