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HypergeometricU




Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Specific values > Specialized values > For fixed z and with symbolical integers in parameters > For fixed z and a=n, b=1/2+-m





http://functions.wolfram.com/07.33.03.0059.01









  


  








Input Form





HypergeometricU[n, 1/2 + m, z] == (-z^(1/2 - m)) E^z ((1/Pochhammer[3/2 - m, n - 1]) Sum[((-1)^k/k!) (Erf[Sqrt[z]] Gamma[-(1/2) + k + m] - Sum[z^(1/2 + j)/Pochhammer[-(1/2) + k + m, 2 + j - k - m], {j, 0, -2 + k + m}]/E^z + Sum[z^(1/2 + j)/Pochhammer[-(1/2) + k + m, 2 + j - k - m], {j, -1 + k + m, -1}]/E^z) LaguerreL[-1 - k + n, k, -z], {k, 0, -1 + n}] + (-1)^n Gamma[1/2 + m - n] LaguerreL[-1 + n, 1/2 - m, -z]) /; 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