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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/03.19.26.0004.01









  


  










Input Form





KelvinKei[\[Nu], z] == (-I) 2^(-1 + \[Nu]) E^((-(-1)^(1/4)) z - (I Pi \[Nu])/4) Sqrt[Pi] z^\[Nu] HypergeometricU[1/2 + \[Nu], 1 + 2 \[Nu], 2 (-1)^(1/4) z] + (I (-1)^(\[Nu]/4) 2^(-1 + \[Nu]) Sqrt[Pi] z^\[Nu] HypergeometricU[1/2 + \[Nu], 1 + 2 \[Nu], 2 (-1)^(3/4) z])/ E^((-1)^(3/4) z) - 2^(-3 - \[Nu]) E^((3 I Pi \[Nu])/4) z^\[Nu] (Pi - 4 I Log[z] + 4 I Log[(-1)^(1/4) z]) Hypergeometric0F1Regularized[ 1 + \[Nu], (I z^2)/4] - (-1)^((5 \[Nu])/4) 2^(-3 - \[Nu]) z^\[Nu] (Pi + 4 I Log[z] - 4 I Log[(-1)^(3/4) z]) Hypergeometric0F1Regularized[ 1 + \[Nu], -((I z^2)/4)] /; Element[\[Nu], Integers]










Standard Form





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MathML Form







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</ci> </apply> <ci> U </ci> </apply> </apply> <apply> <plus /> <ci> &#957; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#957; </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <cn type='integer'> -1 </cn> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> &#957; </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02