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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 Bessel I





http://functions.wolfram.com/03.20.26.0074.01









  


  








Input Form





BesselI[\[Nu], (-1)^(1/4) z] KelvinKer[\[Nu], z] == ((1/8) Sqrt[Pi] ((-1)^(1/4) z)^\[Nu] (MeijerG[{{}, {(3 \[Nu] + 1)/2}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2), (3 \[Nu] + 1)/2}}, z/(2 Sqrt[2]), 1/4] + I MeijerG[{{}, {(3 \[Nu])/2}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2), (3 \[Nu])/2}}, z/(2 Sqrt[2]), 1/4] + (1/(Pi Sqrt[2])) (MeijerG[{{1/4, 3/4}, {}}, {{0, \[Nu]/2, (\[Nu] + 1)/2}, {1/2, -(\[Nu]/2), (1 - \[Nu])/2}}, z/2, 1/4] - I MeijerG[{{1/4, 3/4}, {}}, {{1/2, \[Nu]/2, (\[Nu] + 1)/2}, {-(\[Nu]/2), 1/2 - \[Nu]/2, 0}}, z/2, 1/4])))/ (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