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WhittakerM






Mathematica Notation

Traditional Notation









Hypergeometric Functions > WhittakerM[nu,mu,z] > Specific values > Specialized values > For fixed z and half-integer parameters > For fixed z and mu=m/2





http://functions.wolfram.com/07.44.03.0044.01









  


  










Input Form





WhittakerM[m/2 + n, m/2, z] == (((-1)^n z^((1 + m)/2) m!)/ (2^m (Pochhammer[1/2, m] Pochhammer[1/2 + m, n]))) Sum[(z^k Binomial[n, k] Pochhammer[1/2 - m - n, -k + n] Sum[(-(1/2))^p Binomial[k + m, p] Sum[Binomial[p, j] BesselI[-2 j + p, z/2], {j, 0, p}], {p, 0, k + m}])/2^k, {k, 0, n}] /; Element[n, Integers] && n >= 0 && Element[m, Integers] && m >= 0










Standard Form





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MathML Form







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</ci> </apply> <apply> <in /> <ci> m </ci> <ci> &#8469; </ci> </apply> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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Contributed by





Brychkov Yu.A. (2006)










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





2007-05-02





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