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Sinh






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.19.20.0010.01









  


  










Input Form





D[Sinh[z]^n, {z, \[Alpha]}] == (I^n Binomial[n, n/2] (1 - Mod[n, 2]) (1/(z^\[Alpha] Gamma[1 - \[Alpha]])))/ 2^n - (2^(\[Alpha] - n) I^n Sqrt[Pi] Sum[(-1)^(k - 1) Binomial[n, k] (2 Cos[(n Pi)/2] HypergeometricPFQRegularized[{1}, {1/2 - \[Alpha]/2, 1 - \[Alpha]/2}, (1/4) (-2 k + n)^2 z^2] - I (-2 k + n) z HypergeometricPFQRegularized[{1}, {1 - \[Alpha]/2, 3/2 - \[Alpha]/2}, (1/4) (-2 k + n)^2 z^2] Sin[(n Pi)/2]), {k, 0, Floor[(n - 1)/2]}])/z^\[Alpha] /; Element[n, Integers] && n > 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)





2002-12-18