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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/01.02.20.0026.01









  


  








Input Form





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