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Cos






Mathematica Notation

Traditional Notation









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





http://functions.wolfram.com/01.07.20.0010.01









  


  










Input Form





D[Cos[z]^n, {z, \[Alpha]}] == (Binomial[n, n/2] (1 - Mod[n, 2]) (1/(z^\[Alpha] Gamma[1 - \[Alpha]])))/ 2^n + (2^(1 + \[Alpha] - n) Sqrt[Pi] Sum[Binomial[n, k] HypergeometricPFQRegularized[{1}, {1/2 - \[Alpha]/2, 1 - \[Alpha]/2}, (-(1/4)) (-2 k + n)^2 z^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