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variants of this functions
Log






Mathematica Notation

Traditional Notation









Elementary Functions > Log[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/01.04.20.0023.01









  


  










Input Form





D[z^a Log[z]^2, {z, \[Alpha]}] == Piecewise[{{2 (-1)^(\[Alpha] - a - 1) (\[Alpha] - a - 1)! Gamma[1 + a] (Log[z] + PolyGamma[1 + a] - PolyGamma[\[Alpha] - a]) z^(a - \[Alpha]), Element[\[Alpha] - a, Integers] && \[Alpha] - a > 0}, {((-1)^a/(3 (-1 - a)! Gamma[1 + a - \[Alpha]])) (-Log[z]^3 + 3 Log[z]^2 (-PolyGamma[-a] + PolyGamma[1 + a - \[Alpha]]) + Log[z] (-Pi^2 - 3 PolyGamma[-a]^2 + 6 PolyGamma[-a] PolyGamma[1 + a - \[Alpha]] - 3 PolyGamma[1 + a - \[Alpha]]^2 + 3 PolyGamma[1, -a] + 3 PolyGamma[1, 1 + a - \[Alpha]]) - PolyGamma[-a]^3 + 3 PolyGamma[-a]^2 PolyGamma[1 + a - \[Alpha]] + PolyGamma[1 + a - \[Alpha]]^3 + PolyGamma[1 + a - \[Alpha]] (Pi^2 - 3 PolyGamma[1, -a] - 3 PolyGamma[1, 1 + a - \[Alpha]]) - PolyGamma[-a] (Pi^2 + 3 PolyGamma[1 + a - \[Alpha]]^2 - 3 PolyGamma[1, -a] - 3 PolyGamma[1, 1 + a - \[Alpha]]) - PolyGamma[2, -a] + PolyGamma[2, 1 + a - \[Alpha]]) z^(a - \[Alpha]), Element[-a, Integers] && -a > 0}}, (Gamma[1 + a]/Gamma[1 + a - \[Alpha]]) ((Log[z] + PolyGamma[1 + a] - PolyGamma[1 + a - \[Alpha]])^2 + PolyGamma[1, 1 + a] - PolyGamma[1, 1 + a - \[Alpha]]) z^(a - \[Alpha])]










Standard Form





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MathML Form







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





2007-05-02





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