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





http://functions.wolfram.com/07.33.03.0078.01









  


  










Input Form





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










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