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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/07.33.03.0060.01









  


  








Input Form





HypergeometricU[n, 1/2 + m, z] == E^z z^(1/2 - m) ((((-1)^n Sqrt[Pi])/(n - 1)!) z^(-1 + n) Erf[Sqrt[z]] Sum[(Binomial[-1 + n, p] Pochhammer[1/2, m - n + p])/(-z)^p, {p, 0, -1 + n}] - (((2 (-1)^n)/(n - 1)!) z^(-(1/2) + m) Sum[(((-1)^p Binomial[-1 + n, p])/(1 + 2 m - 2 n + 2 p)) Sum[Pochhammer[-(1/2) - m + n - p, k]/(-z)^k, {k, 1, m - n + p}], {p, 0, -1 + n}])/E^z - (-1)^n Gamma[1/2 + m - n] LaguerreL[-1 + n, 1/2 - m, -z]) /; 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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Date Added to functions.wolfram.com (modification date)





2007-05-02