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; }

 Coth

 http://functions.wolfram.com/01.22.21.0184.01

 Input Form

 Integrate[Cos[a z]^m Cosh[b z]^u Coth[c z], z] == (1/c) (2^(-m - u) Binomial[m, m/2] Binomial[u, u/2] Log[Sinh[c z]] (1 - Mod[m, 2]) (1 - Mod[u, 2])) - 2^(-m - u) Binomial[u, u/2] (1 - Mod[u, 2]) Sum[Binomial[m, k] ((I ((2 c - I a (-2 k + m)) Hypergeometric2F1[-((I a (-2 k + m))/(2 c)), 1, 1 - (I a (-2 k + m))/(2 c), E^(2 c z)] - I a E^(2 c z) (-2 k + m) Hypergeometric2F1[ 1 - (I a (-2 k + m))/(2 c), 1, 2 - (I a (-2 k + m))/(2 c), E^(2 c z)]))/E^(I a (-2 k + m) z)/(a (-2 k + m) (2 c - I a (-2 k + m))) - (I E^(I a (-2 k + m) z) ((2 c + I a (-2 k + m)) Hypergeometric2F1[(I a (-2 k + m))/(2 c), 1, 1 + (I a (-2 k + m))/(2 c), E^(2 c z)] + I a E^(2 c z) (-2 k + m) Hypergeometric2F1[1 + (I a (-2 k + m))/(2 c), 1, 2 + (I a (-2 k + m))/(2 c), E^(2 c z)]))/ (a (-2 k + m) (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[Binomial[u, k] (-(((2 c - b (-2 k + u)) Hypergeometric2F1[-((b (-2 k + u))/(2 c)), 1, 1 - (b (-2 k + u))/(2 c), E^(2 c z)] - b E^(2 c z) (-2 k + u) Hypergeometric2F1[1 - (b (-2 k + u))/(2 c), 1, 2 - (b (-2 k + u))/(2 c), E^(2 c z)])/E^(b (-2 k + u) z)/ (b (-2 k + u) (2 c - b (-2 k + u)))) + (E^(b (-2 k + u) z) ((2 c + b (-2 k + u)) Hypergeometric2F1[ (b (-2 k + u))/(2 c), 1, 1 + (b (-2 k + u))/(2 c), E^(2 c z)] + b E^(2 c z) (-2 k + u) Hypergeometric2F1[1 + (b (-2 k + u))/(2 c), 1, 2 + (b (-2 k + u))/(2 c), E^(2 c z)]))/ (b (-2 k + u) (2 c + b (-2 k + u)))), {k, 0, Floor[(1/2) (-1 + u)]}] - 2^(-m - u) Sum[Binomial[m, k] Binomial[u, s] ((E^(((-I) a (-2 k + m) - b (-2 s + u)) z) ((2 c - I a (-2 k + m) - b (-2 s + u)) 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)] + E^(2 c z) ((-I) a (-2 k + m) - b (-2 s + u)) 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)]))/ (((-I) a (-2 k + m) - b (-2 s + u)) (2 c - I a (-2 k + m) - b (-2 s + u))) + (E^((I a (-2 k + m) - b (-2 s + u)) z) ((2 c + I a (-2 k + m) - b (-2 s + u)) 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)] + E^(2 c z) (I a (-2 k + m) - b (-2 s + u)) 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)]))/ ((I a (-2 k + m) - b (-2 s + u)) (2 c + I a (-2 k + m) - b (-2 s + u))) + (E^(((-I) a (-2 k + m) + b (-2 s + u)) z) ((2 c - I a (-2 k + m) + b (-2 s + u)) 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)] + E^(2 c z) ((-I) a (-2 k + m) + b (-2 s + u)) 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)]))/ (((-I) a (-2 k + m) + b (-2 s + u)) (2 c - I a (-2 k + m) + b (-2 s + u))) + (E^((I a (-2 k + m) + b (-2 s + u)) z) ((2 c + I a (-2 k + m) + b (-2 s + u)) 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)] + E^(2 c z) (I a (-2 k + m) + b (-2 s + u)) 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)]))/ ((I a (-2 k + m) + b (-2 s + u)) (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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 Date Added to functions.wolfram.com (modification date)

 2002-12-18

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