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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/03.19.06.0014.01









  


  










Input Form





KelvinKei[\[Nu], z] \[Proportional] ((-2^(-1 + \[Nu])) Sin[(3 Pi \[Nu])/4] Gamma[\[Nu]] (1 - z^4/(32 (-2 + \[Nu]) (-1 + \[Nu])) + z^8/(6144 (-4 + \[Nu]) (-3 + \[Nu]) (-2 + \[Nu]) (-1 + \[Nu])) + \[Ellipsis]))/z^\[Nu] - 2^(-1 - \[Nu]) z^\[Nu] Sin[(Pi \[Nu])/4] Gamma[-\[Nu]] (1 - z^4/(32 (1 + \[Nu]) (2 + \[Nu])) + z^8/(6144 (1 + \[Nu]) (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu])) + \[Ellipsis]) - 2^(-3 + \[Nu]) z^(2 - \[Nu]) Cos[(3 Pi \[Nu])/4] Gamma[\[Nu] - 1] (1 - z^4/(96 (-3 + \[Nu]) (-2 + \[Nu])) + z^8/(30720 (-5 + \[Nu]) (-4 + \[Nu]) (-3 + \[Nu]) (-2 + \[Nu])) + \[Ellipsis]) - 2^(-3 - \[Nu]) z^(2 + \[Nu]) Cos[(Pi \[Nu])/4] Gamma[-1 - \[Nu]] (1 - z^4/(96 (2 + \[Nu]) (3 + \[Nu])) + z^8/(30720 (2 + \[Nu]) (3 + \[Nu]) (4 + \[Nu]) (5 + \[Nu])) + \[Ellipsis]) /; (z -> 0) && !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> <cn type='integer'> -2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 30720 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -5 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -4 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -3 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#915; </ci> <ci> &#957; </ci> <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> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; 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</ci> </apply> <cn type='integer'> -1 </cn> </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> <ci> Gamma </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> </apply> <apply> <power /> <ci> z </ci> <ci> &#957; </ci> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 32 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 6144 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </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'> -3 </cn> </apply> </apply> <apply> <cos /> <apply> <times /> <pi /> <ci> &#957; </ci> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <ci> Gamma </ci> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <apply> <power /> <ci> z </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 96 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 30720 </cn> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 2 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 3 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 4 </cn> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 5 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <ci> &#8230; </ci> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <ci> Rule </ci> <ci> z </ci> <cn type='integer'> 0 </cn> </apply> <apply> <notin /> <ci> &#957; </ci> <integers /> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02





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