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variants of this functions
KelvinKer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKer[nu,z] > Representations through more general functions > Through hypergeometric functions > Involving hypergeometric U





http://functions.wolfram.com/03.20.26.0003.01









  


  










Input Form





KelvinKer[\[Nu], z] == (2^(-2 - \[Nu]) E^((I Pi \[Nu])/4) Pi Csc[Pi \[Nu]] (-z^(2 \[Nu]) + E^((I Pi \[Nu])/2) ((-1)^(3/4) z)^(2 \[Nu])) Hypergeometric0F1Regularized[1 + \[Nu], -((I z^2)/4)])/z^\[Nu] - (2^(-2 - \[Nu]) Pi Csc[Pi \[Nu]] (E^((I Pi \[Nu])/2) z^(2 \[Nu]) - ((-1)^(1/4) z)^(2 \[Nu])) Hypergeometric0F1Regularized[1 + \[Nu], (I z^2)/4])/(E^((3 I Pi \[Nu])/4) z^\[Nu]) + (2^(-1 + \[Nu]) E^((-(-1)^(1/4)) z - (3 I Pi \[Nu])/4) Sqrt[Pi] ((-1)^(1/4) z)^(2 \[Nu]) HypergeometricU[1/2 + \[Nu], 1 + 2 \[Nu], 2 (-1)^(1/4) z])/z^\[Nu] + (2^(-1 + \[Nu]) E^((-(-1)^(3/4)) z + (3 I Pi \[Nu])/4) Sqrt[Pi] ((-1)^(3/4) z)^(2 \[Nu]) HypergeometricU[1/2 + \[Nu], 1 + 2 \[Nu], 2 (-1)^(3/4) z])/z^\[Nu] /; !Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <ci> z </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> </apply> </apply> </apply> <apply> <ci> Hypergeometric0F1Regularized </ci> <apply> <plus /> <ci> &#957; </ci> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <imaginaryi /> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <cn type='integer'> 4 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <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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