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WhittakerW




Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerW[nu,mu,z] > Series representations > Generalized power series > Expansions at z==0 > Logarithmic case





http://functions.wolfram.com/07.45.06.0017.01









  


  








Input Form





WhittakerW[\[Nu], \[Mu], z] \[Proportional] (((-1)^(2 \[Mu]) z^(1/2 + \[Mu]))/Gamma[1/2 - \[Mu] - \[Nu]]) (((2 \[Mu] - 1)!/(z^(2 \[Mu]) Pochhammer[1/2 - \[Mu] + \[Nu], 2 \[Mu]])) (1 + O[z]) - (Log[z]/(2 \[Mu])!) (1 + O[z]) + (-Sum[((-1)^j 2^(-1 - j) j!)/((1 + j)! (2 \[Mu] - j - 1)! Pochhammer[1/2 - \[Mu] + \[Nu], 1 + j]), {j, 0, 2 \[Mu] - 1}] + (-EulerGamma + PolyGamma[1 + 2 \[Mu]] - PolyGamma[1/2 + \[Mu] - \[Nu]])/ (2 \[Mu])!) (1 + O[z])) /; 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