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Sin






Mathematica Notation

Traditional Notation









Elementary Functions > Sin[z] > Differentiation > Fractional integro-differentiation





http://functions.wolfram.com/01.06.20.0015.01









  


  










Input Form





D[(z^\[Beta] Sin[z])^a, {z, \[Alpha]}] == E^(2 I a Pi Floor[1/2 - Arg[Sin[z]/z]/(2 Pi) - Im[(\[Beta] + 1) Log[z]]/ (2 Pi)]) a z^((\[Beta] + 1) a - \[Alpha]) Sum[Binomial[k - a, k] Sum[(((-1)^j Binomial[k, j])/(a - j)) Subscript[p, j, k] FDPowerConstant[z, (\[Beta] + 1) a + k, \[Alpha]] z^k, {j, 0, k}], {k, 0, Infinity}] /; Subscript[p, j, 0] == 1 && Subscript[p, j, k] == (1/k) Sum[(j m - k + m) (1 + 2 Floor[m/2] - m) ((-1)^(m/2)/(m + 1)!) Subscript[p, j, k - m], {m, 1, 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