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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function > Involving products of powers of the direct function > Involving product of power of the direct function and the direct function > Involving cosh(b z) coshv(c zr)





http://functions.wolfram.com/01.20.21.2147.01









  


  










Input Form





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