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variants of this functions
KelvinKei




Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > General case





http://functions.wolfram.com/03.19.06.0020.01









  


  








Input Form





KelvinKei[\[Nu], z] \[Proportional] Piecewise[{{-Pi/4, \[Nu] == 0}, {(-(-1)^(Abs[\[Nu]]/4)) 2^(-3 + Abs[\[Nu]]) z^(2 - Abs[\[Nu]]) (-2 + Abs[\[Nu]])!, Element[\[Nu]/4, Integers]}, {((-1 + I) (-1)^(\[Nu] - 1) (-1)^(\[Nu]/4) 2^(-2 + Abs[\[Nu]]) (-1 + Abs[\[Nu]])!)/z^Abs[\[Nu]], Element[(\[Nu] - 1)/4, Integers]}, {((-1)^UnitStep[(\[Nu] - 2)/4] I (-1)^(\[Nu]/4) 2^(-1 + Abs[\[Nu]]) (-1 + Abs[\[Nu]])!)/z^Abs[\[Nu]], Element[(\[Nu] - 2)/4, Integers]}, {((1 + I) (-1)^(\[Nu] - 1) (-1)^(\[Nu]/4) 2^(-2 + Abs[\[Nu]]) (-1 + Abs[\[Nu]])!)/z^Abs[\[Nu]], Element[(\[Nu] - 3)/4, Integers]}}, (-2^(-1 - \[Nu])) z^\[Nu] Gamma[-\[Nu]] Sin[(Pi \[Nu])/4] - (2^(-1 + \[Nu]) Gamma[\[Nu]] Sin[(3 Pi \[Nu])/4])/z^\[Nu]] /; (z -> 0)








Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <abs /> <ci> &#957; </ci> </apply> <cn type='integer'> -2 </cn> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <abs /> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <factorial /> <apply> <plus /> <apply> <abs /> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <in /> <apply> <times /> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> <integers /> </apply> </piece> <otherwise> <apply> <plus /> <apply> <times /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <ci> &#957; </ci> </apply> <apply> <sin /> <apply> <times /> <cn type='integer'> 3 </cn> <pi /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <sin /> <apply> <times /> <pi /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> &#957; </ci> </apply> </apply> </apply> </apply> </otherwise> </piecewise> </apply> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02