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variants of this functions
PolyGamma






Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > PolyGamma[z] > Integration > Definite integration > Involving the direct function





http://functions.wolfram.com/06.14.21.0004.01









  


  










Input Form





Integrate[PolyGamma[t + 1] (z - t)^(n - 1), {t, 0, z}] == (n - 1)! PolyGamma[-n, z + 1] - Sum[(-1)^k Binomial[n - 1, k] (z + 1)^(n - 1 - k) Sum[(-1)^j Pochhammer[k - j + 1, j] PolyGamma[-j - 1, 1], {j, 0, k}], {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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Date Added to functions.wolfram.com (modification date)





2007-05-02