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Power






Mathematica Notation

Traditional Notation









Elementary Functions > Power[z,a] > Differentiation > Fractional integro-differentiation > With respect to z





http://functions.wolfram.com/01.02.20.0027.01









  


  










Input Form





D[(b z^c)^a, {z, \[Alpha]}] == Piecewise[{{((-1)^\[Alpha] Pochhammer[(-a) c, \[Alpha]] (b z^c)^a)/ z^\[Alpha], Element[\[Alpha], Integers] && Element[a c, Integers] && a c < 0 && a c < \[Alpha]}, {((((-1)^(a c - 1) (Log[b z^c] + c PolyGamma[(-a) c] - c PolyGamma[1 + a c - \[Alpha]]))/(c (-1 - a c)! Gamma[1 + a c - \[Alpha]])) (b z^c)^a)/z^\[Alpha], Element[a c, Integers] && a c < 0}}, ((Gamma[1 + a c]/Gamma[1 - \[Alpha] + a c]) (b z^c)^a)/z^\[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





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