html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 Csch

 http://functions.wolfram.com/01.23.21.0219.01

 Input Form

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