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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 Meijer G > Generalized cases involving 0F~1





http://functions.wolfram.com/03.20.26.0079.01









  


  










Input Form





Hypergeometric0F1Regularized[\[Nu] + 1, (I z^2)/4] KelvinKer[\[Nu], z] == ((1/8) Sqrt[Pi] ((I MeijerG[{{}, {(5 \[Nu])/4}}, {{(2 - \[Nu])/4, -(\[Nu]/4), \[Nu]/4}, {-((3 \[Nu])/4), (5 \[Nu])/4}}, z/(2 Sqrt[2]), 1/4] + MeijerG[{{}, {(2 + 5 \[Nu])/4}}, {{(2 - \[Nu])/4, -(\[Nu]/4), \[Nu]/4}, {-((3 \[Nu])/4), (2 + 5 \[Nu])/4}}, z/(2 Sqrt[2]), 1/4])/ 2^(\[Nu]/2) + (1/(Sqrt[2] Pi)) ((-I) MeijerG[{{(1 - \[Nu])/4, (3 - \[Nu])/4}, {}}, {{(2 - \[Nu])/4, \[Nu]/4, (2 + \[Nu])/4}, {(2 - 3 \[Nu])/4, -((3 \[Nu])/4), -(\[Nu]/4)}}, z/2, 1/4] + MeijerG[{{(1 - \[Nu])/4, (3 - \[Nu])/4}, {}}, {{-(\[Nu]/4), \[Nu]/4, (2 + \[Nu])/4}, {(2 - 3 \[Nu])/4, (2 - \[Nu])/4, -((3 \[Nu])/4)}}, z/2, 1/4])))/E^((3/4) I Pi \[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