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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/07.45.20.0013.01









  


  










Input Form





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










Standard Form





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MathML Form







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</ci> </apply> <ci> &#956; </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <notin /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> &#956; </ci> </apply> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Date Added to functions.wolfram.com (modification date)





2007-05-02





© 1998- Wolfram Research, Inc.