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variants of this functions
PolyGamma




Mathematica Notation

Traditional Notation









Gamma, Beta, Erf > PolyGamma[nu,z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving power function





http://functions.wolfram.com/06.15.21.0002.01









  


  








Input Form





Integrate[z^(\[Alpha] - 1) PolyGamma[\[Nu], z], z] == (z^(\[Alpha] - \[Nu] - 1)/((\[Alpha] - \[Nu] - 1) Gamma[-\[Nu]])) (1/(\[Alpha] - \[Nu] - 1) + EulerGamma + PolyGamma[-\[Nu]] - Log[z]) + (z^(1 + \[Alpha] - \[Nu])/((1 + \[Alpha] - \[Nu]) Gamma[2 - \[Nu]])) Sum[(1/(k + 1)^2) HypergeometricPFQ[{1, 2, 1 + \[Alpha] - \[Nu]}, {2 - \[Nu], 2 + \[Alpha] - \[Nu]}, -(z/(k + 1))], {k, 0, Infinity}] - (EulerGamma z^(\[Alpha] - \[Nu]))/(Gamma[1 - \[Nu]] (\[Alpha] - \[Nu]))








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