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variants of this functions
KelvinKei






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKei[nu,z] > Series representations > Generalized power series > Expansions at z==0 > For the function itself > Logarithmic cases





http://functions.wolfram.com/03.19.06.0030.01









  


  










Input Form





KelvinKei[\[Nu], z] == 4^(-3 - Abs[\[Nu]]) Pi^2 z^(2 + Abs[\[Nu]]) Sin[(1/4) Pi (2 \[Nu] + Abs[\[Nu]])] HypergeometricPFQRegularized[{}, {3/2, (1/2) (2 + Abs[\[Nu]]), (1/2) (3 + Abs[\[Nu]])}, -(z^4/256)] - 4^(-1 - Abs[\[Nu]]) Pi^2 z^Abs[\[Nu]] Cos[(1/4) Pi (2 \[Nu] + Abs[\[Nu]])] HypergeometricPFQRegularized[{}, {1/2, (1/2) (1 + Abs[\[Nu]]), (1/2) (2 + Abs[\[Nu]])}, -(z^4/256)] + ((1/4) I Sum[(1/k!) (E^((1/4) I Pi (2 \[Nu] + Abs[\[Nu]])) - (-1)^k/E^((1/4) (I Pi (2 \[Nu] + Abs[\[Nu]])))) (Abs[\[Nu]] - k - 1)! ((I z^2)/4)^k, {k, 0, Abs[\[Nu]] - 1}])/(z/2)^Abs[\[Nu]] + (1/4) I ((I z)/2)^Abs[\[Nu]] E^((I Pi \[Nu])/2) Sum[(1/(k! (k + Abs[\[Nu]])!)) (E^((-(1/4)) (I Pi Abs[\[Nu]])) - (-1)^k E^((1/4) I Pi Abs[\[Nu]])) (2 Log[z/2] - PolyGamma[1 + k] - PolyGamma[1 + k + Abs[\[Nu]]]) ((I z^2)/4)^k, {k, 0, Infinity}] /; 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





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