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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 zr)cosh(c zr)





http://functions.wolfram.com/01.20.21.1228.01









  


  










Input Form





Integrate[E^(p z^2) Sin[b z^2]^m Cosh[c z^2], z] == 2^(-2 - m) Sqrt[Pi] Binomial[m, m/2] (Erfi[Sqrt[-c + p] z]/Sqrt[-c + p] + Erfi[Sqrt[c + p] z]/Sqrt[c + p]) (1 - Mod[m, 2]) + 2^(-2 - m) Sqrt[Pi] Sum[(-1)^k Binomial[m, k] (Cos[(m Pi)/2] (Erfi[Sqrt[-c + 2 I b k - I b m + p] z]/ Sqrt[-c + 2 I b k - I b m + p] + Erfi[Sqrt[c + 2 I b k - I b m + p] z]/Sqrt[c + 2 I b k - I b m + p] + Erfi[Sqrt[-c - 2 I b k + I b m + p] z]/ Sqrt[-c - 2 I b k + I b m + p] + Erfi[Sqrt[c - 2 I b k + I b m + p] z]/Sqrt[c - 2 I b k + I b m + p]) + I (Erfi[Sqrt[-c + 2 I b k - I b m + p] z]/ Sqrt[-c + 2 I b k - I b m + p] + Erfi[Sqrt[c + 2 I b k - I b m + p] z]/Sqrt[c + 2 I b k - I b m + p] - Erfi[Sqrt[-c - 2 I b k + I b m + p] z]/ Sqrt[-c - 2 I b k + I b m + p] - Erfi[Sqrt[c - 2 I b k + I b m + p] z]/Sqrt[c - 2 I b k + I b m + p]) Sin[(m Pi)/2]), {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='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> p </ci> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <ci> c </ci> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> c </ci> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <power /> <pi /> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <ci> Binomial </ci> <ci> m </ci> <apply> <times /> <ci> m </ci> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='integer'> -1 </cn> </apply> </apply> </apply> <apply> <plus /> <cn type='integer'> 1 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<ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <ci> z </ci> </apply> </apply> <apply> <power /> <apply> <power /> <apply> <plus /> <ci> c </ci> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> </apply> <apply> <times /> <imaginaryi /> <ci> b </ci> <ci> m </ci> </apply> <ci> p </ci> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <ci> Erfi </ci> <apply> <times /> <apply> <power /> <apply> <plus /> <apply> <times /> <cn type='integer'> -1 </cn> <ci> c </ci> </apply> <apply> <times /> <cn type='integer'> 2 </cn> <imaginaryi /> <ci> b </ci> <ci> k </ci> </apply> 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Rule Form





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





2002-12-18