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HypergeometricU






Mathematica Notation

Traditional Notation









Hypergeometric Functions > HypergeometricU[a,b,z] > Differentiation > Low-order differentiation > With respect to a





http://functions.wolfram.com/07.33.20.0019.01









  


  










Input Form





Derivative[1, 0, 0][HypergeometricU][a, a + n, z] == (-HypergeometricU[a, a + n, z]) (Log[z] + PolyGamma[a]) + Sum[Binomial[n - 1, k] z^(-a - k) Pochhammer[a, k] PolyGamma[a + k], {k, 0, n - 1}] - (1/Gamma[a]) Sum[Binomial[n - 1, k] (((-1)^k Pi Csc[a Pi] Hypergeometric1F1[a + k, 1 + a + k, z])/(a + k) - (Gamma[a + k]/z^(a + k)) (Log[z] - PolyGamma[a + k] - (z HypergeometricPFQ[{1, 1}, {2, 2 - a - k}, z])/(a + k - 1))), {k, 0, n - 1}] /; Element[n, Integers] && n > 0










Standard Form





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MathML Form







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Rule Form





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Contributed by





Brychkov Yu.A. (2007)










Date Added to functions.wolfram.com (modification date)





2007-05-02