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; }

 Tanh

 http://functions.wolfram.com/01.21.21.0163.01

 Input Form

 Integrate[Cos[a z]^m Sinh[b z]^u Tanh[c z], z] == (1/c) I^u 2^(-m - u) Binomial[m, m/2] Binomial[u, u/2] Log[Cosh[c z]] (1 - Mod[m, 2]) (1 - Mod[u, 2]) - I^u 2^(-m - u) Binomial[u, u/2] (-1 + Mod[u, 2]) Sum[Binomial[m, k] (-((1/(a (-2 k + m))) ((I Hypergeometric2F1[-((I a (-2 k + m))/(2 c)), 1, 1 - (I a (-2 k + m))/(2 c), -E^(2 c z)])/ E^(I a (-2 k + m) z))) + (1/(a (-2 k + m))) (I E^(I a (-2 k + m) z) Hypergeometric2F1[(I a (-2 k + m))/(2 c), 1, 1 + (I a (-2 k + m))/(2 c), -E^(2 c z)]) + (E^((2 c - I a (-2 k + m)) z) Hypergeometric2F1[ 1 - (I a (-2 k + m))/(2 c), 1, 2 - (I a (-2 k + m))/(2 c), -E^(2 c z)])/(2 c - I a (-2 k + m)) + (E^((2 c + I a (-2 k + m)) z) Hypergeometric2F1[ 1 + (I a (-2 k + m))/(2 c), 1, 2 + (I a (-2 k + m))/(2 c), -E^(2 c z)])/(2 c + I a (-2 k + m))), {k, 0, Floor[(1/2) (-1 + m)]}] + 2^(-m - u) Binomial[m, m/2] (1 - Mod[m, 2]) Sum[(-1)^k Binomial[u, k] (-((1/(b (-2 k + u))) (E^(b (-2 k + u) z) Hypergeometric2F1[ (b (-2 k + u))/(2 c), 1, 1 + (b (-2 k + u))/(2 c), -E^(2 c z)])) + (-1)^u ((1/(b (-2 k + u))) (Hypergeometric2F1[-((b (-2 k + u))/(2 c)), 1, 1 - (b (-2 k + u))/(2 c), -E^(2 c z)]/E^(b (-2 k + u) z)) + (E^((2 c - b (-2 k + u)) z) Hypergeometric2F1[ 1 - (b (-2 k + u))/(2 c), 1, 2 - (b (-2 k + u))/(2 c), -E^(2 c z)])/(2 c - b (-2 k + u))) + (E^((2 c + b (-2 k + u)) z) Hypergeometric2F1[ 1 + (b (-2 k + u))/(2 c), 1, 2 + (b (-2 k + u))/(2 c), -E^(2 c z)])/ (2 c + b (-2 k + u))), {k, 0, Floor[(1/2) (-1 + u)]}] + 2^(-m - u) Sum[(-1)^s Binomial[m, k] Binomial[u, s] (-((E^(((-I) a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), 1, 1 + ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ ((-I) a (-2 k + m) + b (-2 s + u))) - (E^((I a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ (I a (-2 k + m) + b (-2 s + u))/(2 c), 1, 1 + (I a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ (I a (-2 k + m) + b (-2 s + u)) + (-1)^u (-((E^(((-I) a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), 1, 1 + ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ ((-I) a (-2 k + m) - b (-2 s + u))) + (E^((2 c - I a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ 1 + ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), 1, 2 + ((-I) a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c - I a (-2 k + m) - b (-2 s + u))) + (-1)^u (-((E^((I a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ (I a (-2 k + m) - b (-2 s + u))/(2 c), 1, 1 + (I a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ (I a (-2 k + m) - b (-2 s + u))) + (E^((2 c + I a (-2 k + m) - b (-2 s + u)) z) Hypergeometric2F1[ 1 + (I a (-2 k + m) - b (-2 s + u))/(2 c), 1, 2 + (I a (-2 k + m) - b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c + I a (-2 k + m) - b (-2 s + u))) + (E^((2 c - I a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ 1 + ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), 1, 2 + ((-I) a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c - I a (-2 k + m) + b (-2 s + u)) + (E^((2 c + I a (-2 k + m) + b (-2 s + u)) z) Hypergeometric2F1[ 1 + (I a (-2 k + m) + b (-2 s + u))/(2 c), 1, 2 + (I a (-2 k + m) + b (-2 s + u))/(2 c), -E^(2 c z)])/ (2 c + I a (-2 k + m) + b (-2 s + u))), {s, 0, Floor[(1/2) (-1 + u)]}, {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