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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/01.04.20.0017.01









  


  










Input Form





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










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





© 1998- Wolfram Research, Inc.