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Cosh






Mathematica Notation

Traditional Notation









Elementary Functions > Cosh[z] > Integration > Indefinite integration > Involving functions of the direct function, trigonometric and exponential functions > Involving powers of the direct function, trigonometric and exponential functions > Involving sin and exp > Involving ep z sin(b zr)coshv(c zr)





http://functions.wolfram.com/01.20.21.3745.01









  


  










Input Form





Integrate[E^(p z) Sin[b Sqrt[z]] Cosh[c Sqrt[z]]^v, z] == 2^(-2 - v) Binomial[v, v/2] (1 - Mod[v, 2]) (-((b E^(b^2/(4 p)) Sqrt[Pi] (Erfi[((-I) b + 2 p Sqrt[z])/(2 Sqrt[p])] + Erfi[(I b + 2 p Sqrt[z])/(2 Sqrt[p])]))/p^(3/2)) + (4 E^(p z) Sin[b Sqrt[z]])/p) - I 2^(-2 - v) Sum[Binomial[v, s] ((1/p^(3/2)) (E^((b + 2 I c s - I c v)^2/(4 p)) Sqrt[Pi] (b + 2 I c s - I c v) (Erf[(b + 2 I c s - I c v - 2 I p Sqrt[z])/(2 Sqrt[p])] - Erf[(b + 2 I c s - I c v + 2 I p Sqrt[z])/(2 Sqrt[p])])) + (1/p^(3/2)) (E^((b + I c (-2 s + v))^2/(4 p)) Sqrt[Pi] (b + I c (-2 s + v)) (Erf[(b - 2 I c s + I c v - 2 I p Sqrt[z])/ (2 Sqrt[p])] - Erf[(b - 2 I c s + I c v + 2 I p Sqrt[z])/ (2 Sqrt[p])])) + (1/p) (4 I E^(p z) (Sin[(b + 2 I c s - I c v) Sqrt[z]] + Sin[(b + I c (-2 s + v)) Sqrt[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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Date Added to functions.wolfram.com (modification date)





2002-12-18