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Cos






Mathematica Notation

Traditional Notation









Elementary Functions > Cos[z] > Series representations > Generalized power series > Expansions at z==0 > For powers of the function > For symbolical integer power





http://functions.wolfram.com/01.07.06.0047.01









  


  










Input Form





Cos[z]^n == Subscript[F, Infinity][z] /; Subscript[F, m][z] == 1 + 2^(1 - n) Sum[(((-1)^j/(2 j)!) Sum[Binomial[n, k] (n - 2 k)^(2 j), {k, 0, Floor[(n - 1)/2]}]) z^(2 j), {j, 1, m}] == Cos[z]^n + (((-1)^m Sqrt[Pi] z^(2 + 2 m))/2^(n + 2 m + 1)) Sum[Binomial[n, k] (n - 2 k)^(2 + 2 m) HypergeometricPFQRegularized[{1}, {3/2 + m, 2 + m}, -(((n - 2 k)^2 z^2)/4)], {k, 0, Floor[(n - 1)/2]}] && Element[m, Integers] && m >= 0 && 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)





2007-05-02





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