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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Representations through more general functions > Through Meijer G > Classical cases involving Bessel I





http://functions.wolfram.com/03.19.26.0042.01









  


  










Input Form





BesselI[\[Nu], (-1)^(1/4) z] KelvinKei[\[Nu], z] == ((1/8) Sqrt[Pi] ((-1)^(1/4) z)^\[Nu] (I MeijerG[{{}, {(3 \[Nu] + 1)/2}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2), (3 \[Nu] + 1)/2}}, z^4/64] - MeijerG[{{}, {(3 \[Nu])/2}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2), (3 \[Nu])/2}}, z^4/64] - (1/(Pi Sqrt[2])) (MeijerG[{{1/4, 3/4}, {}}, {{1/2, \[Nu]/2, (\[Nu] + 1)/2}, {-(\[Nu]/2), (1 - \[Nu])/2, 0}}, z^4/16] + I MeijerG[{{1/4, 3/4}, {}}, {{0, \[Nu]/2, (\[Nu] + 1)/2}, {1/2, -(\[Nu]/2), (1 - \[Nu])/2}}, z^4/16])))/ (E^((3/4) I Pi \[Nu]) z^\[Nu]) /; -(Pi/4) <= Arg[z] <= Pi/4










Standard Form





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MathML Form







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</ci> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> <ci> &#957; </ci> </apply> <apply> <plus /> <apply> <times /> <imaginaryi /> <apply> <ci> MeijerG </ci> <list> <list /> <list> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> </apply> </list> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </list> <list> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> 3 </cn> <ci> &#957; 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Rule Form





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





2007-05-02





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