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WhittakerM




Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.44.20.0003.01









  


  








Input Form





Derivative[0, 1, 0][WhittakerM][\[Nu], \[Mu], z] == z^(\[Mu] + 1/2) Sum[Sum[(((-1)^(k - j) 2^(-k + j))/(k - j)!) (Pochhammer[\[Mu] - \[Nu] + 1/2, j]/(Pochhammer[2 \[Mu] + 1, j] j!)) (-2 PolyGamma[1 + j + 2 \[Mu]] + PolyGamma[1/2 + j + \[Mu] - \[Nu]]), {j, 0, k}] z^k, {k, 0, Infinity}] + (Log[z] + 2 PolyGamma[1 + 2 \[Mu]] - PolyGamma[1/2 + \[Mu] - \[Nu]]) WhittakerM[\[Nu], \[Mu], z]








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