Hyperbolic secant: Integration (formula 01.24.21.0107)

Sech

$Mathematica Notation$

Elementary Functions

Sech[z]

Integration

Indefinite integration

Involving one direct function and elementary functions

Involving hyperbolic functions

Involving power of cosh

Involving cosh^mu(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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Rule Form

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

2002-12-18