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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/07.44.03.0057.01









  


  










Input Form





WhittakerM[(2 m - 1)/4 + n, (2 m - 1)/4, z] == ((-1)^m ((1 - 2 m)/2) z^((5 - 2 m)/4) Sum[((-1)^k/k!) LaguerreL[m + n - k - 1, k, z] ((Erfi[Sqrt[z]] Gamma[-(1/2) + k + m])/Sqrt[z] - E^z Sum[(-z)^j/Pochhammer[-(1/2) + k + m, 2 + j - k - m], {j, 0, k + m - 2}]), {k, 0, m + n - 1}])/E^(z/2) /; 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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Date Added to functions.wolfram.com (modification date)





2007-05-02