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variants of this functions
KelvinKer




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKer[z] > Representations through more general functions > Through Meijer G > Generalized cases involving Bessel J





http://functions.wolfram.com/03.16.26.0039.01









  


  








Input Form





BesselJ[0, (-1)^(1/4) z] KelvinKer[z] == (1/8) Sqrt[Pi] (MeijerG[{{}, {}}, {{0, 0}, {0, 1/2}}, z/(2 Sqrt[2]), 1/4] - I MeijerG[{{}, {}}, {{0, 1/2}, {0, 0}}, z/(2 Sqrt[2]), 1/4] + (1/(Sqrt[2] Pi)) (MeijerG[{{1/4, 3/4}, {}}, {{0, 0, 1/2}, {0, 1/2, 1/2}}, z/2, 1/4] + I MeijerG[{{1/4, 3/4}, {}}, {{0, 1/2, 1/2}, {0, 0, 1/2}}, z/2, 1/4]))








Standard Form





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MathML Form







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<list> <list /> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <ci> MeijerG </ci> <list> <list /> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> </list> </list> <apply> <times /> <ci> z </ci> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> 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MeijerG </ci> <list> <list> <cn type='rational'> 1 <sep /> 4 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </list> <list /> </list> <list> <list> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> <list> <cn type='integer'> 0 </cn> <cn type='integer'> 0 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </list> </list> <apply> <times /> <ci> z </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02