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Coth




Mathematica Notation

Traditional Notation









Elementary Functions > Coth[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/01.22.21.0103.01









  


  








Input Form





Integrate[Cosh[b z]^m Coth[c z], z] == (Binomial[m, m/2] Log[Sinh[c z]] (1 - Mod[m, 2]))/(2^m c) - Sum[Binomial[m, s] (-(((2 c - b (-2 s + m)) Hypergeometric2F1[-((b (-2 s + m))/(2 c)), 1, 1 - (b (-2 s + m))/(2 c), E^(2 c z)] - b E^(2 c z) (-2 s + m) Hypergeometric2F1[1 - (b (-2 s + m))/(2 c), 1, 2 - (b (-2 s + m))/(2 c), E^(2 c z)])/E^(b (-2 s + m) z))/ (b (-2 s + m) (2 c - b (-2 s + m))) + (E^(b (-2 s + m) z) ((2 c + b (-2 s + m)) Hypergeometric2F1[ (b (-2 s + m))/(2 c), 1, 1 + (b (-2 s + m))/(2 c), E^(2 c z)] + b E^(2 c z) (-2 s + m) Hypergeometric2F1[1 + (b (-2 s + m))/(2 c), 1, 2 + (b (-2 s + m))/(2 c), E^(2 c z)]))/ (b (-2 s + m) (2 c + b (-2 s + m)))), {s, 0, Floor[(1/2) (-1 + m)]}]/ 2^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