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 Csch

 http://functions.wolfram.com/01.23.21.0208.01

 Input Form

 Integrate[Sin[a z]^m Cosh[b z]^u Csch[c z], z] == (-((2^(1 - m - u) E^(c z) Binomial[m, m/2] Binomial[u, u/2])/c)) HypergeometricPFQ[{1/2, 1}, {3/2}, E^(2 c z)] (1 - Mod[m, 2]) (1 - Mod[u, 2]) - 2^(1 - m - u) E^(c z) Binomial[u, u/2] (1 - Mod[u, 2]) Sum[(-1)^s Binomial[m, s] ((1/(I a (m - 2 s) + c)) (E^((-(1/2)) I m Pi + I a (m - 2 s) z) HypergeometricPFQ[ {(I a m)/(2 c) - (I a s)/c + 1/2, 1}, {(I a m)/(2 c) - (I a s)/c + 3/2}, E^(2 c z)]) + (E^((I m Pi)/2 - I a (m - 2 s) z) HypergeometricPFQ[{-((I a m)/(2 c)) + (I a s)/c + 1/2, 1}, {-((I a m)/(2 c)) + (I a s)/c + 3/2}, E^(2 c z)])/ ((-I) a (m - 2 s) + c)), {s, 0, Floor[(1/2) (-1 + m)]}] - 2^(1 - m - u) E^(c z) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[Binomial[u, k] (HypergeometricPFQ[{(b k)/c - (b u)/(2 c) + 1/2, 1}, {(b k)/c - (b u)/(2 c) + 3/2}, E^(2 c z)]/E^(b (-2 k + u) z)/ ((-b) (-2 k + u) + c) + (1/(b (-2 k + u) + c)) (E^(b (-2 k + u) z) HypergeometricPFQ[{-((b k)/c) + (b u)/(2 c) + 1/2, 1}, {-((b k)/c) + (b u)/(2 c) + 3/2}, E^(2 c z)])), {k, 0, Floor[(1/2) (-1 + u)]}] - 2^(1 - m - u) E^(c z) Sum[(-1)^s Binomial[m, s] Binomial[u, k] ((E^((-(1/2)) I m Pi + (I a (m - 2 s) - b (-2 k + u)) z) HypergeometricPFQ[{(b k)/c + (I a m)/(2 c) - (I a s)/c - (b u)/(2 c) + 1/2, 1}, {(b k)/c + (I a m)/(2 c) - (I a s)/c - (b u)/(2 c) + 3/2}, E^(2 c z)])/(I a (m - 2 s) - b (-2 k + u) + c) + (E^((I m Pi)/2 + ((-I) a (m - 2 s) - b (-2 k + u)) z) HypergeometricPFQ[{(b k)/c - (I a m)/(2 c) + (I a s)/c - (b u)/(2 c) + 1/2, 1}, {(b k)/c - (I a m)/(2 c) + (I a s)/c - (b u)/(2 c) + 3/2}, E^(2 c z)])/((-I) a (m - 2 s) - b (-2 k + u) + c) + (E^((-(1/2)) I m Pi + (I a (m - 2 s) + b (-2 k + u)) z) HypergeometricPFQ[{-((b k)/c) + (I a m)/(2 c) - (I a s)/c + (b u)/(2 c) + 1/2, 1}, {-((b k)/c) + (I a m)/(2 c) - (I a s)/c + (b u)/(2 c) + 3/2}, E^(2 c z)])/(I a (m - 2 s) + b (-2 k + u) + c) + (E^((I m Pi)/2 + ((-I) a (m - 2 s) + b (-2 k + u)) z) HypergeometricPFQ[{-((b k)/c) - (I a m)/(2 c) + (I a s)/c + (b u)/(2 c) + 1/2, 1}, {-((b k)/c) - (I a m)/(2 c) + (I a s)/c + (b u)/(2 c) + 3/2}, E^(2 c z)])/((-I) a (m - 2 s) + b (-2 k + u) + c)), {k, 0, Floor[(1/2) (-1 + u)]}, {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0

 Standard Form

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 MathML Form

 Rule Form

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

 2002-12-18