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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/07.44.03.0063.01









  


  










Input Form





WhittakerM[-((2 m + 1)/4) + n, -((2 m + 1)/4), z] == ((-1)^m ((2 m + 1)/2) z^((5 + 2 m)/4) Sum[((-1)^k/k!) LaguerreL[-1 - k - m + n, 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, -2 + k - m}] + E^z Sum[(-z)^(-j - 1)/Pochhammer[ -(1/2) + k - m, 1 - j - k + m], {j, 0, -k + m}]), {k, 0, -1 - m + n}])/E^(z/2) /; Element[n, Integers] && Element[m, Integers] && n > m










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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