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Sech






Mathematica Notation

Traditional Notation









Elementary Functions > Sech[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving hyperbolic functions > Involving power of cosh > Involving coshmu(b z)





http://functions.wolfram.com/01.24.21.0107.01









  


  










Input Form





Integrate[Cosh[b z]^m Sech[c z], z] == Binomial[m, m/2] (1 - Mod[m, 2]) ((2^(1 - m) ArcTan[E^(c z)])/c) + 2^(1 - m) Sum[Binomial[m, s] ((1/(c + b (m - 2 s))) (E^((c + b (m - 2 s)) z) Hypergeometric2F1[1, (c + b m - 2 b s)/ (2 c), (3 c + b m - 2 b s)/(2 c), -E^(2 c z)]) + (1/(c - b m + 2 b s)) (E^((c - b m + 2 b s) z) Hypergeometric2F1[1, (c - b m + 2 b s)/(2 c), (3 c - b m + 2 b s)/(2 c), -E^(2 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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</apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <ci> c </ci> <ci> z </ci> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> </apply> <apply> <in /> <ci> m </ci> <integers /> </apply> </apply> </annotation-xml> </semantics> </math>










Rule Form





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





2002-12-18





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