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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=+-m





http://functions.wolfram.com/07.33.03.0038.01









  


  










Input Form





HypergeometricU[n, -m, z] == E^z (m + 1) Sum[(((-1)^q z^(n + m - p - q) (m + k)!)/(p! k! (n - p - q - 1)! (m + n - p)! (q - k)!)) (Sum[z^j/Pochhammer[q - k - m - 1, m - q + k + 2 + j], {j, 0, q - k - m - 2}]/E^z - Sum[z^j/Pochhammer[q - k - m - 1, m - q + k + 2 + j], {j, q - k - m - 1, -1}]/E^z + ((-1)^(m + q - k)/(m + 1 - q + k)!) (CoshIntegral[z] - SinhIntegral[z])), {p, 0, n - 1}, {q, 0, n - 1}, {k, 0, q}] /; 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