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variants of this functions
KelvinBer




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.18.26.0045.01









  


  








Input Form





BesselK[\[Nu], (-1)^(1/4) z] KelvinBer[\[Nu], z] == ((1/4) (-Pi^(3/2)) z^\[Nu] (Sqrt[2] Csc[Pi (\[Nu] + 3/4)] E^((3 I Pi \[Nu])/4) MeijerG[{{1/2}, {1/4, \[Nu] - 1/4}}, {{0, \[Nu]}, {-\[Nu], 1/4, \[Nu] - 1/4}}, I z^2] - (1/(E^((3 I Pi \[Nu])/4) (2 Pi^2))) MeijerG[{{}, {}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2)}}, -(z^4/64)]))/ ((-1)^(1/4) z)^\[Nu] /; Inequality[-(Pi/2), Less, Arg[z], LessEqual, 0]








Standard Form





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MathML Form







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</mo> <mrow> <mrow> <mo> - </mo> <mfrac> <mi> &#960; </mi> <mn> 2 </mn> </mfrac> </mrow> <mo> &lt; </mo> <mrow> <mi> arg </mi> <mo> &#8289; </mo> <mo> ( </mo> <mi> z </mi> <mo> ) </mo> </mrow> <mo> &#8804; </mo> <mn> 0 </mn> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <ci> Condition </ci> <apply> <eq /> <apply> <times /> <apply> <ci> BesselK </ci> <ci> &#957; </ci> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <ci> KelvinBer </ci> <ci> &#957; </ci> <ci> z </ci> </apply> </apply> <apply> <times /> <cn type='rational'> 1 <sep /> 4 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <pi /> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> &#957; </ci> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 1 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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Rule Form





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





2007-05-02