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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/07.44.03.0053.01









  


  










Input Form





WhittakerM[(2 m + 1)/4 - n, (2 m - 1)/4, z] == (1/2) Pochhammer[3/2, -1 + m] (Sqrt[Pi] Erf[Sqrt[z]] E^(z/2) z^((3 - 2 m)/4) Sum[Binomial[-m + n, k] LaguerreL[-1 + k + m, 1/2 - k - m, -z], {k, 0, -m + n}] + (z^((5 - 2 m)/4) Sum[Binomial[-m + n, k] Sum[(1/p) LaguerreL[-1 + k + m - p, 1/2 - k - m + p, -z] LaguerreL[-1 + p, 1/2 - p, z], {p, 1, -1 + k + m}], {k, 0, -m + n}])/E^(z/2)) /; Element[n, Integers] && Element[m, Integers] && m > 0 && m <= n










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





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