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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=2m+-1/4





http://functions.wolfram.com/07.44.03.0049.01









  


  










Input Form





WhittakerM[(2 m + 1)/4 + n, (2 m + 1)/4, z] == ((1/2) (-1)^m Sqrt[Pi] z^((1 - 2 m)/4) Erfi[Sqrt[z]] Pochhammer[3/2, m] Sum[Binomial[n, k] LaguerreL[k + m, -(1/2) - k - m, z], {k, 0, n}])/ E^(z/2) + (1/2) (-1)^m E^(z/2) z^((3 - 2 m)/4) Pochhammer[3/2, m] Sum[Binomial[n, k] Sum[(1/p) LaguerreL[k + m - p, -(1/2) - k - m + p, z] LaguerreL[-1 + p, 1/2 - p, -z], {p, 1, k + m}], {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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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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