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variants of this functions
KelvinKer






Mathematica Notation

Traditional Notation









Bessel-Type Functions > KelvinKer[nu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/03.20.20.0018.01









  


  










Input Form





D[KelvinKer[\[Nu], z], {z, \[Alpha]}] == ((2^(-2 + \[Nu]) Pi z^(-\[Alpha] - \[Nu]) Csc[Pi \[Nu]])/ (E^((3/4) I Pi \[Nu]) Gamma[1 - \[Alpha] - \[Nu]])) (E^((3 I Pi \[Nu])/2) HypergeometricPFQ[{(1 - \[Nu])/2, 1 - \[Nu]/2}, {1 - \[Nu], (1 - \[Alpha] - \[Nu])/2, 1 - (\[Alpha] + \[Nu])/2}, -((I z^2)/4)] + HypergeometricPFQ[{(1 - \[Nu])/2, 1 - \[Nu]/2}, {1 - \[Nu], (1 - \[Alpha] - \[Nu])/2, 1 - (\[Alpha] + \[Nu])/2}, (I z^2)/4]) - ((2^(-2 - \[Nu]) Pi z^(-\[Alpha] + \[Nu]) Csc[Pi \[Nu]])/ (E^((1/4) I Pi \[Nu]) Gamma[1 - \[Alpha] + \[Nu]])) (E^((I Pi \[Nu])/2) HypergeometricPFQ[{(1 + \[Nu])/2, 1 + \[Nu]/2}, {1 + \[Nu], (1 - \[Alpha] + \[Nu])/2, 1 - (\[Alpha] - \[Nu])/2}, -((I z^2)/4)] + HypergeometricPFQ[{(1 + \[Nu])/2, 1 + \[Nu]/2}, {1 + \[Nu], (1 - \[Alpha] + \[Nu])/2, 1 - (\[Alpha] - \[Nu])/2}, (I z^2)/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