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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 Meijer G > Classical cases involving 0F~1





http://functions.wolfram.com/03.19.26.0049.01









  


  








Input Form





Hypergeometric0F1Regularized[\[Nu] + 1, (I Sqrt[z])/4] KelvinKei[\[Nu], z^(1/4)] == (2^(-3 + \[Nu]) Sqrt[Pi] (I MeijerG[{{}, {(3 \[Nu] + 1)/2}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2), (3 \[Nu] + 1)/2}}, z/64] - MeijerG[{{}, {(3 \[Nu])/2}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2), (3 \[Nu])/2}}, z/64] - (1/(Pi Sqrt[2])) (MeijerG[{{1/4, 3/4}, {}}, {{1/2, \[Nu]/2, (\[Nu] + 1)/2}, {-(\[Nu]/2), (1 - \[Nu])/2, 0}}, z/16] + I MeijerG[{{1/4, 3/4}, {}}, {{0, \[Nu]/2, (\[Nu] + 1)/2}, {1/2, -(\[Nu]/2), (1 - \[Nu])/2}}, z/16])))/ (E^((3/4) I Pi \[Nu]) z^\[Nu])








Standard Form





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MathML Form







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Rule Form





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





2007-05-02