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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+1/2, b=1/2-m





http://functions.wolfram.com/07.33.03.0069.01









  


  










Input Form





HypergeometricU[n + 1/2, 1/2 - m, z] == (-1)^(m + n) E^z Gamma[1/2 - n] LaguerreL[m + n, -(1/2) - m, -z] - (((-1)^m Sqrt[Pi])/Gamma[1/2 + n]) (E^z Sqrt[Pi] Erf[Sqrt[z]] Sum[Binomial[n, k] LaguerreL[k + m, -(1/2) - k - m, -z], {k, 0, n}] + Sqrt[z] Sum[Binomial[n, k] Sum[(1/p) LaguerreL[k + m - p, -(1/2) - k - m + p, -z] LaguerreL[-1 + p, 1/2 - p, z], {p, 1, k + m}], {k, 0, n}]) /; 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