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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+k/4





http://functions.wolfram.com/07.44.03.0061.01









  


  










Input Form





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