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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/01.02.20.0028.01









  


  










Input Form





D[f[z]^a, {z, \[Alpha]}] == E^(2 I a Pi Floor[1/2 - Arg[f[0]]/(2 Pi) - (1/(2 Pi)) Arg[f[z]/f[0]]]) (a/Gamma[1 - a]) f[0]^a Sum[(Gamma[1 + k - a]/Gamma[1 + k - \[Alpha]]) Sum[(((-1)^j Binomial[k, j])/(a - j)) Subscript[p, j, k] z^(k - \[Alpha]), {j, 0, k}], {k, 0, Infinity}] /; Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/(f[0] k)) Sum[((j m - k + m)/m!) Derivative[m][f][0] Subscript[p, j, k - m], {m, 1, k}] && Element[k, Integers] && k > 0 && f[0] != 0










Standard Form





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MathML Form







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Rule Form





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2007-05-02





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