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HypergeometricU






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/07.33.20.0017.01









  


  










Input Form





D[HypergeometricU[a, -n, z], {z, \[Alpha]}] == ((-1)^n/(z^\[Alpha] Gamma[a])) ((1/(n + 1)!) Sum[((Pochhammer[a + n + 1, k] z^(k + n + 1))/ (Pochhammer[n + 2, k] k!)) FDLogConstant[z, k + n + 1, \[Alpha]], {k, 0, Infinity}] - Sum[(Pochhammer[a, k] (-1)^(k + n - 1) (n - k)! z^k)/(Pochhammer[a, n + 1] Gamma[k - \[Alpha] + 1]), {k, 0, n}] + Sum[(Pochhammer[a + n + 1, k]/(Gamma[k + n + 2 - \[Alpha]] k!)) (PolyGamma[a + n + k + 1] - PolyGamma[1 + k] - PolyGamma[n + k + 2]) z^(k + n + 1), {k, 0, Infinity}]) /; Element[n, Integers] && n > 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)





2001-10-29





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