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; }

 Sech

 http://functions.wolfram.com/01.24.21.0214.01

 Input Form

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