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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.19.07.0001.01









  


  










Input Form





KelvinKei[\[Nu], z] == (-(1/(8 Pi I))) ContourIntegral[ (Gamma[s + \[Nu]/4] Gamma[s - \[Nu]/4] Gamma[s + (\[Nu] + 2)/4] Gamma[s + (2 - \[Nu])/4])/(Gamma[\[Nu]/2 + s] Gamma[1 - \[Nu]/2 - s])/ (z/4)^(4 s), \[ScriptCapitalL]["s"]]










Standard Form





Cell[BoxData[RowBox[List[RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]", ",", "z"]], "]"]], "\[Equal]", RowBox[List[RowBox[List["-", FractionBox["1", RowBox[List["8", "\[Pi]", " ", "\[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["\[Nu]", "4"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["\[Nu]", "+", "2"]], "4"]]], "]"]], RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["2", "-", "\[Nu]"]], "4"]]], "]"]]]], RowBox[List[RowBox[List["Gamma", "[", RowBox[List[FractionBox["\[Nu]", "2"], "+", "s"]], "]"]], RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]]]]], SuperscriptBox[RowBox[List["(", FractionBox["z", "4"], ")"]], RowBox[List[RowBox[List["-", "4"]], "s"]]], RowBox[List["\[DifferentialD]", "s"]]]]]]]]]]]]










MathML Form







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</mi> <mo> + </mo> <mn> 2 </mn> </mrow> <mn> 4 </mn> </mfrac> <mo> + </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> + </mo> <mfrac> <mrow> <mn> 2 </mn> <mo> - </mo> <mi> &#957; </mi> </mrow> <mn> 4 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> </mrow> <mrow> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mi> s </mi> <mo> + </mo> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> ) </mo> </mrow> <mo> &#8290; </mo> <mrow> <mi> &#915; </mi> <mo> &#8289; </mo> <mo> ( </mo> <mrow> <mn> 1 </mn> <mo> - </mo> <mfrac> <mi> &#957; </mi> <mn> 2 </mn> </mfrac> <mo> - </mo> <mi> s </mi> </mrow> <mo> ) </mo> </mrow> </mrow> </mfrac> <mo> &#8290; </mo> <msup> <mrow> <mo> ( </mo> <mfrac> <mi> z </mi> <mn> 4 </mn> </mfrac> <mo> ) </mo> </mrow> <mrow> <mrow> <mo> - </mo> <mn> 4 </mn> </mrow> <mo> &#8290; </mo> <mi> s </mi> </mrow> </msup> <mo> &#8290; </mo> <mrow> <mo> &#8518; 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</ms> <ms> 4 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#915; </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> s </ms> <ms> - </ms> <apply> <ci> FractionBox </ci> <ms> &#957; </ms> <ms> 4 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#915; </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> &#957; </ms> <ms> + </ms> <ms> 2 </ms> </list> </apply> <ms> 4 </ms> </apply> <ms> + </ms> <ms> s </ms> </list> </apply> <ms> ) </ms> </list> </apply> <apply> <ci> RowBox </ci> <list> <ms> &#915; </ms> <ms> ( </ms> <apply> <ci> RowBox </ci> <list> <ms> s </ms> <ms> + </ms> <apply> <ci> FractionBox </ci> <apply> <ci> RowBox </ci> <list> <ms> 2 </ms> <ms> - </ms> <ms> &#957; </ms> </list> </apply> <ms> 4 </ms> </apply> </list> </apply> <ms> ) </ms> </list> </apply> </list> </apply> <apply> <ci> RowBox </ci> <list> <apply> <ci> RowBox </ci> <list> <ms> &#915; 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Rule Form





Cell[BoxData[RowBox[List[RowBox[List["HoldPattern", "[", RowBox[List["KelvinKei", "[", RowBox[List["\[Nu]_", ",", "z_"]], "]"]], "]"]], "\[RuleDelayed]", RowBox[List["-", 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["\[Nu]", "4"]]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["s", "+", FractionBox[RowBox[List["\[Nu]", "+", "2"]], "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[FractionBox["\[Nu]", "2"], "+", "s"]], "]"]], " ", RowBox[List["Gamma", "[", RowBox[List["1", "-", FractionBox["\[Nu]", "2"], "-", "s"]], "]"]]]]], ",", RowBox[List["\[ScriptCapitalL]", "[", "\"s\"", "]"]]]], "]"]], RowBox[List["8", " ", "\[Pi]", " ", "\[ImaginaryI]"]]]]]]]]]










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





2007-05-02





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