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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 and exponential functions > Involving powers of sin and exp > Involving ep zr sinm(b z)cosh(c z)





http://functions.wolfram.com/01.20.21.1217.01









  


  










Input Form





Integrate[E^(p z^2) Sin[b z]^m Cosh[c z], z] == (1/Sqrt[p]) (2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] (Erfi[(-c + 2 p z)/(2 Sqrt[p])]/E^(c^2/(4 p)) + Erfi[(c + 2 p z)/(2 Sqrt[p])]/E^(c^2/(4 p))) (1 - Mod[m, 2])) + (1/Sqrt[p]) (2^(-2 - m) Sqrt[Pi] Sum[(-1)^k Binomial[m, k] (Erfi[(-c - I b (2 k - m) + 2 p z)/(2 Sqrt[p])]/ E^(((-c - I b (2 k - m))^2 + 2 I m p Pi)/(4 p)) + Erfi[(c + I b (2 k - m) + 2 p z)/(2 Sqrt[p])]/ E^(((c + I b (2 k - m))^2 - 2 I m p Pi)/(4 p)) + Erfi[(-c - I b (-2 k + m) + 2 p z)/(2 Sqrt[p])]/ E^(((-c - I b (-2 k + m))^2 - 2 I m p Pi)/(4 p)) + Erfi[(c + I b (-2 k + m) + 2 p z)/(2 Sqrt[p])]/ E^(((c + I b (-2 k + m))^2 + 2 I m p Pi)/(4 p))), {k, 0, Floor[(1/2) (-1 + m)]}]) /; Element[m, Integers] && m > 0










Standard Form





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MathML Form







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type='integer'> 4 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <ci> z </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> p </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <apply> <power /> <ci> c </ci> <cn type='integer'> 2 </cn> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> p </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <rem /> <ci> $CellContext`m </ci> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <power /> <ci> p </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <power /> <ci> p </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> <cn type='integer'> -2 </cn> </apply> 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2 </cn> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> <imaginaryi /> <ci> m </ci> <ci> p </ci> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 4 </cn> <ci> p </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <plus /> <ci> c </ci> <apply> <times /> <ci> b </ci> <imaginaryi /> <apply> <plus /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> k </ci> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <ci> m </ci> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <ci> p </ci> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> p </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times 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Rule Form





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Date Added to functions.wolfram.com (modification date)





2002-12-18