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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/01.04.20.0015.01









  


  










Input Form





D[Log[z]^n, {z, \[Alpha]}] == Piecewise[{{((-1)^(\[Alpha] - 1) n! Sum[(Log[z]^(u - i)/(u - i)!) (Derivative[n - 1 - u][Gamma][1]/(n - 1 - u)!) Sum[Subscript[a, v] Subscript[b, i - v], {v, 0, i}], {u, 0, n - 1}, {i, 0, u}])/z^\[Alpha], Element[\[Alpha], Integers] && \[Alpha] > 0}}, D[(Gamma[1 + a]/Gamma[1 + a - \[Alpha]]) z^(a - \[Alpha]), {a, n}] /; a == 0] /; Element[n, Integers] && n > 0 && Subscript[a, 2 k] == ((-1)^k Pi^(2 k))/(2 k + 1)! && Subscript[a, 2 k + 1] == 0 && Subscript[b, k] == ((-1)^k Derivative[k][Gamma][\[Alpha]])/k! && Element[k, Integers] && k > 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





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