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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 K





http://functions.wolfram.com/03.20.26.0076.01









  


  








Input Form





BesselK[\[Nu], (-1)^(1/4) z] KelvinKer[\[Nu], z] == ((E^((3 I Pi \[Nu])/4) Pi^(5/2) z^\[Nu] (-I + Cot[Pi \[Nu]]) Csc[Pi (3/4 + \[Nu])])/(((-1)^(1/4) z)^\[Nu] (4 Sqrt[2]))) MeijerG[{{1/2}, {1/4, -(1/4) + \[Nu]}}, {{0, \[Nu]}, {1/4, -\[Nu], -(1/4) + \[Nu]}}, (-1)^(1/4) z, 1/2] - ((Pi^(5/2) ((-1)^(1/4) z)^\[Nu] Csc[Pi \[Nu]])/(E^((3 I Pi \[Nu])/4) z^\[Nu] (4 Sqrt[2]))) Csc[Pi (\[Nu] + 1/4)] MeijerG[{{1/2}, {1/4, -\[Nu] - 1/4}}, {{0, -\[Nu]}, {\[Nu], 1/4, -\[Nu] - 1/4}}, (-1)^(1/4) z, 1/2] - ((1/16) Sqrt[Pi] z^\[Nu] (I + Cot[Pi \[Nu]]) MeijerG[{{}, {}}, {{0, 1/2, \[Nu]/2}, {-(\[Nu]/2)}}, ((-1)^(1/4) z)/(2 Sqrt[2]), 1/4])/ (E^((3/4) I Pi \[Nu]) ((-1)^(1/4) z)^\[Nu]) + ((E^((3 I Pi \[Nu])/4) Sqrt[Pi] ((-1)^(1/4) z)^\[Nu] Csc[Pi \[Nu]])/ (z^\[Nu] 16)) MeijerG[{{}, {}}, {{0, 1/2, -(\[Nu]/2)}, {\[Nu]/2}}, ((-1)^(1/4) z)/(2 Sqrt[2]), 1/4] /; !Element[\[Nu], Integers]








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