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 Csch

 http://functions.wolfram.com/01.23.21.0263.01

 Input Form

 Integrate[E^(p z) Sin[a z]^m Coth[c z]^u Csch[c z], z] == 2^(-m - u) (1 - E^(2 c z))^(u + 1) Binomial[m, m/2] Csch[c z]^(u + 1) (1 - Mod[m, 2]) ((1/(p + c (u + 1))) (E^(p z) Binomial[u, u/2] HypergeometricPFQ[{(c (u + 1) + p)/(2 c), u + 1}, {1 + (c (u + 1) + p)/(2 c)}, E^(2 c z)] (1 - Mod[u, 2])) + Sum[Binomial[u, s] ((1/(p + c (2 s + 1))) (E^((p - c (-2 s + u)) z) HypergeometricPFQ[{(c (2 s + 1) + p)/(2 c), u + 1}, {1 + (c (2 s + 1) + p)/(2 c)}, E^(2 c z)]) + (E^((p + c (-2 s + u)) z) HypergeometricPFQ[ {(c (2 u - 2 s + 1) + p)/(2 c), u + 1}, {1 + (c (2 u - 2 s + 1) + p)/(2 c)}, E^(2 c z)])/ (p + c (-2 s + 2 u + 1))), {s, 0, Floor[(1/2) (-1 + u)]}]) + 2^(-m - u) (1 - E^(2 c z))^(u + 1) Csch[c z]^(u + 1) Sum[(-1)^k Binomial[m, k] (E^((I m Pi)/2) ((E^(((-I) a (-2 k + m) + p) z) Binomial[u, u/2] HypergeometricPFQ[ {(c (u + 1) + ((-I) a (-2 k + m) + p))/(2 c), u + 1}, {1 + (c (u + 1) + ((-I) a (-2 k + m) + p))/(2 c)}, E^(2 c z)] (1 - Mod[u, 2]))/((-I) a (-2 k + m) + p + c (u + 1)) + Sum[Binomial[u, s] ((E^(((-I) a (-2 k + m) + p - c (-2 s + u)) z) HypergeometricPFQ[{(c (2 s + 1) + ((-I) a (-2 k + m) + p))/ (2 c), u + 1}, {1 + (c (2 s + 1) + ((-I) a (-2 k + m) + p))/ (2 c)}, E^(2 c z)])/((-I) a (-2 k + m) + p + c (2 s + 1)) + (E^(((-I) a (-2 k + m) + p + c (-2 s + u)) z) HypergeometricPFQ[{ (c (2 u - 2 s + 1) + ((-I) a (-2 k + m) + p))/(2 c), u + 1}, { 1 + (c (2 u - 2 s + 1) + ((-I) a (-2 k + m) + p))/(2 c)}, E^ (2 c z)])/((-I) a (-2 k + m) + p + c (-2 s + 2 u + 1))), {s, 0, Floor[(1/2) (-1 + u)]}]) + ((E^((I a (-2 k + m) + p) z) Binomial[u, u/2] HypergeometricPFQ[ {(c (u + 1) + (I a (-2 k + m) + p))/(2 c), u + 1}, {1 + (c (u + 1) + (I a (-2 k + m) + p))/(2 c)}, E^(2 c z)] (1 - Mod[u, 2]))/(I a (-2 k + m) + p + c (u + 1)) + Sum[Binomial[u, s] ((E^((I a (-2 k + m) + p - c (-2 s + u)) z) HypergeometricPFQ[{(c (2 s + 1) + (I a (-2 k + m) + p))/(2 c), u + 1}, {1 + (c (2 s + 1) + (I a (-2 k + m) + p))/(2 c)}, E^ (2 c z)])/(I a (-2 k + m) + p + c (2 s + 1)) + (E^((I a (-2 k + m) + p + c (-2 s + u)) z) HypergeometricPFQ[{ (c (2 u - 2 s + 1) + (I a (-2 k + m) + p))/(2 c), u + 1}, { 1 + (c (2 u - 2 s + 1) + (I a (-2 k + m) + p))/(2 c)}, E^ (2 c z)])/(I a (-2 k + m) + p + c (-2 s + 2 u + 1))), {s, 0, Floor[(1/2) (-1 + u)]}])/E^((1/2) I m Pi)), {k, 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