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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/07.44.03.0050.01









  


  








Input Form





WhittakerM[(2 m + 1)/4 - n, (2 m - 1)/4, z] == ((2 m - 1)/2) E^(z/2) z^((3 - 2 m)/4) Sum[((-1)^k/k!) (Gamma[-(1/2) + k + m] - Gamma[-(1/2) + k + m, z]) LaguerreL[n - k - 1, k, -z], {k, 0, n - 1}] /; Element[n, Integers] && n > 0 && Element[m, Integers]








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