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variants of this functions
KelvinBer




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.18.07.0007.01









  


  








Input Form





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








Standard Form





Cell[BoxData[RowBox[List[RowBox[List["KelvinBer", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[FractionBox["1", RowBox[List["2", "\[ImaginaryI]"]]], RowBox[List[SubscriptBox["\[Integral]", "\[ScriptCapitalL]"], RowBox[List[FractionBox[RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox["\[Nu]", "4"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "4"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List["s", "+", "\[Nu]", "+", FractionBox["1", "2"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List[FractionBox["1", "2"], "-", "s", "-", "\[Nu]"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List[RowBox[List["-", "s"]], "+", FractionBox[RowBox[List["2", "+", "\[Nu]"]], "4"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", "s", "+", FractionBox["\[Nu]", "4"]]], "]"]]]]], SuperscriptBox[RowBox[List["(", FractionBox["z", "4"], ")"]], RowBox[List[RowBox[List["-", "4"]], "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]]]]








MathML Form







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Rule Form





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


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





2007-05-02