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Coth






Mathematica Notation

Traditional Notation









Elementary Functions > Coth[z] > Integration > Indefinite integration > Involving one direct function and elementary functions > Involving trigonometric and exponential functions > Involving powers of cos and exp > Involving ep z cosm(b z)





http://functions.wolfram.com/01.22.21.0058.01









  


  










Input Form





Integrate[E^(p z) Cos[b z]^m Coth[c z], z] == ((-(1/(p (2 c + p)))) E^(p z) Binomial[m, m/2] ((2 c + p) Hypergeometric2F1[p/(2 c), 1, 1 + p/(2 c), E^(2 c z)] + E^(2 c z) p Hypergeometric2F1[1 + p/(2 c), 1, 2 + p/(2 c), E^(2 c z)]) (1 - Mod[m, 2]))/2^m - Sum[Binomial[m, k] ((E^(((-I) b (-2 k + m) + p) z) ((2 c - I b (-2 k + m) + p) Hypergeometric2F1[ ((-I) b (-2 k + m) + p)/(2 c), 1, 1 + ((-I) b (-2 k + m) + p)/ (2 c), E^(2 c z)] + E^(2 c z) ((-I) b (-2 k + m) + p) Hypergeometric2F1[1 + ((-I) b (-2 k + m) + p)/(2 c), 1, 2 + ((-I) b (-2 k + m) + p)/(2 c), E^(2 c z)]))/ (((-I) b (-2 k + m) + p) (2 c - I b (-2 k + m) + p)) + (E^((I b (-2 k + m) + p) z) ((2 c + I b (-2 k + m) + p) Hypergeometric2F1[(I b (-2 k + m) + p)/(2 c), 1, 1 + (I b (-2 k + m) + p)/(2 c), E^(2 c z)] + E^(2 c z) (I b (-2 k + m) + p) Hypergeometric2F1[ 1 + (I b (-2 k + m) + p)/(2 c), 1, 2 + (I b (-2 k + m) + p)/ (2 c), E^(2 c z)]))/((I b (-2 k + m) + p) (2 c + I b (-2 k + m) + p))), {k, 0, Floor[(1/2) (-1 + m)]}]/2^m /; Element[m, Integers] && m > 0










Standard Form





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Rule Form





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





2002-12-18





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