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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/07.45.20.0016.01









  


  










Input Form





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










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





© 1998- Wolfram Research, Inc.