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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric functions > Involving powers of cos > Involving cosm(b zr) cosh(c z)





http://functions.wolfram.com/01.20.21.0779.01









  


  










Input Form





Integrate[Cos[b Sqrt[z]]^m Cosh[c z], z] == ((-(1/2))^m Binomial[m, m/2] (1 - Mod[m, 2]) Sinh[c z])/c + 2^(-1 - m) Sum[Binomial[m, s] ((1/((-I) c)^(3/2)) ((-b) Sqrt[2 Pi] (m - 2 s) (Cosh[(b m - 2 b s)^2/(4 c)] FresnelC[(b (m - 2 s) - 2 I c Sqrt[z])/(Sqrt[(-I) c] Sqrt[ 2 Pi])] + I FresnelS[(b (m - 2 s) - 2 I c Sqrt[z])/ (Sqrt[(-I) c] Sqrt[2 Pi])] Sinh[(b m - 2 b s)^2/(4 c)]) + 2 Sqrt[(-I) c] Sin[(b m - 2 b s) Sqrt[z] - I c z]) + (1/((-I) c)^(3/2)) (b Sqrt[2 Pi] (m - 2 s) (Cosh[(b m - 2 b s)^2/(4 c)] FresnelC[((-b) (m - 2 s) - 2 I c Sqrt[z])/(Sqrt[(-I) c] Sqrt[2 Pi])] + I FresnelS[((-b) (m - 2 s) - 2 I c Sqrt[z])/(Sqrt[(-I) c] Sqrt[ 2 Pi])] Sinh[(b m - 2 b s)^2/(4 c)]) - 2 Sqrt[(-I) c] Sin[(-((-b) m + 2 b s)) Sqrt[z] + I c z])), {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 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