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WhittakerW






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.45.20.0001.01









  


  










Input Form





Derivative[1, 0, 0][WhittakerW][\[Nu], \[Mu], z] == (PolyGamma[1/2 - \[Mu] - \[Nu]] + PolyGamma[1/2 + \[Mu] - \[Nu]]) WhittakerW[\[Nu], \[Mu], z] - ((Gamma[-2 \[Mu]]/Gamma[1/2 - \[Mu] - \[Nu]]) z^(\[Mu] + 1/2) Sum[(Pochhammer[1/2 + \[Mu] - \[Nu], k]/(Pochhammer[2 \[Mu] + 1, k] k!)) PolyGamma[1/2 + k + \[Mu] - \[Nu]] z^k, {k, 0, Infinity}])/E^(z/2) - ((Gamma[2 \[Mu]]/Gamma[1/2 + \[Mu] - \[Nu]]) z^(1/2 - \[Mu]) Sum[(Pochhammer[1/2 - \[Mu] - \[Nu], k]/(Pochhammer[1 - 2 \[Mu], k] k!)) PolyGamma[1/2 + k - \[Mu] - \[Nu]] z^k, {k, 0, Infinity}])/E^(z/2) /; !Element[2 \[Mu], 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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