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WhittakerW






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerW[nu,mu,z] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/07.45.20.0014.01









  


  










Input Form





D[WhittakerW[\[Nu], 0, z], {z, \[Alpha]}] == (-(z^(1/2 - \[Alpha])/Gamma[1/2 - \[Nu]])) (Sum[(((-1)^(-j + k) 2^(j - k) Pochhammer[1/2 - \[Nu], j])/ (j!^2 (-j + k)!)) FDLogConstant[z, k + 1/2, \[Alpha]] z^k, {k, 0, Infinity}, {j, 0, k}] - Sum[(((-1)^(-j + k) 2^(j - k) Pochhammer[1/2 - \[Nu], j] Gamma[k + 3/2])/ (j!^2 (-j + k)! Gamma[k + 3/2 - \[Alpha]])) (2 PolyGamma[1 + j] - PolyGamma[1/2 + j - \[Nu]]) z^k, {k, 0, Infinity}, {j, 0, k}])










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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