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WhittakerW






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerW[nu,mu,z] > Specific values > Specialized values > For fixed z and integer parameters





http://functions.wolfram.com/07.45.03.0032.01









  


  










Input Form





WhittakerW[m/2 - n, (m - 1)/2, z] == (m - 1) z^(m/2) E^(z/2) Sum[(((-1)^q z^(n - p - q - m) (m + k - 2)!)/(p! k! (n - m - p - q)! (n - p - 1)! (q - k)!)) (Sum[z^j/Pochhammer[q - k - m + 1, m - q + k + j], {j, 0, q - k - m}]/ E^z - Sum[z^j/Pochhammer[q - k - m + 1, m - q + k + j], {j, q - k - m + 1, -1}]/E^z + ((-1)^(m + q - k)/(m - q + k - 1)!) (ExpIntegralEi[-z] - (1/2) (Log[-z] - Log[-(1/z)]) + Log[z])), {p, 0, n - m}, {q, 0, n - m}, {k, 0, q}] /; Element[n, Integers] && n > 1 && Element[m, Integers] && Inequality[1, Less, m, LessEqual, n]










Standard Form





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MathML Form







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Pochhammer </ci> <apply> <plus /> <ci> q </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> 1 </cn> </apply> <apply> <plus /> <ci> j </ci> <ci> k </ci> <ci> m </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> q </ci> </apply> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <and /> <apply> <in /> <ci> n </ci> <integers /> </apply> <apply> <gt /> <ci> n </ci> <cn type='integer'> 1 </cn> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> <apply> <ci> Inequality </ci> <cn type='integer'> 1 </cn> <lt /> <ci> m </ci> <leq /> <ci> n </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2007-05-02