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/01.23.21.0276.01

 Input Form

 Integrate[z^n Cos[a z]^m Tanh[c z]^u Csch[c z], z] == I^(-1 + u) 2^(1 - m) E^(c u z) Binomial[m, m/2] Binomial[-1 + u, (1/2) (-1 + u)] n! (1 - Mod[m, 2]) (1 - Mod[-1 + u, 2]) Sum[(1/(-j + n)!) ((-1)^j (c u)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[a, 1], \[Ellipsis], Subscript[a, 1 + j], u}, {1 + Subscript[a, 1], \[Ellipsis], 1 + Subscript[a, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + I^(-1 + u) 2^(1 - m) Binomial[-1 + u, (1/2) (-1 + u)] n! (1 - Mod[-1 + u, 2]) Sum[Binomial[m, k] (E^(((-I) a (-2 k + m) + c u) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a (-2 k + m) + c u)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[b, 1], \[Ellipsis], Subscript[b, 1 + j], u}, {1 + Subscript[b, 1], \[Ellipsis], 1 + Subscript[b, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + E^((I a (-2 k + m) + c u) z) Sum[(1/(-j + n)!) ((-1)^j (I a (-2 k + m) + c u)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[c, 1], \[Ellipsis], Subscript[c, 1 + j], u}, {1 + Subscript[c, 1], \[Ellipsis], 1 + Subscript[c, 1 + j]}, -E^(2 c z)]), {j, 0, n}]), {k, 0, Floor[(1/2) (-1 + m)]}] + 2^(1 - m) E^(c u z) Binomial[m, m/2] n! (1 - Mod[m, 2]) Sum[(-1)^k Binomial[-1 + u, k] (E^(c (-1 - 2 k + u) z) Sum[(1/(-j + n)!) ((-1)^j (c (-1 - 2 k + 2 u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[d, 1], \[Ellipsis], Subscript[d, 1 + j], u}, {1 + Subscript[d, 1], \[Ellipsis], 1 + Subscript[d, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + ((-1)^(-1 + u) Sum[(1/(-j + n)!) ((-1)^j (c (1 + 2 k))^(-1 - j) z^(-j + n) HypergeometricPFQ[ {Subscript[e, 1], \[Ellipsis], Subscript[e, 1 + j], u}, {1 + Subscript[e, 1], \[Ellipsis], 1 + Subscript[e, 1 + j]}, -E^(2 c z)]), {j, 0, n}])/E^(c (-1 - 2 k + u) z)), {k, 0, Floor[(1/2) (-2 + u)]}] + 2^(1 - m) E^(c u z) n! Sum[Binomial[m, k] Sum[(-1)^i Binomial[-1 + u, i] (E^(((-I) a (-2 k + m) + c (-1 - 2 i + u)) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a (-2 k + m) + c (-1 - 2 i + 2 u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[f, 1], \[Ellipsis], Subscript[f, 1 + j], u}, {1 + Subscript[f, 1], \[Ellipsis], 1 + Subscript[f, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + (-1)^(-1 + u) E^(((-I) a (-2 k + m) - c (-1 - 2 i + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c (1 + 2 i) - I a (-2 k + m))^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[g, 1], \[Ellipsis], Subscript[g, 1 + j], u}, {1 + Subscript[g, 1], \[Ellipsis], 1 + Subscript[g, 1 + j]}, -E^(2 c z)]), {j, 0, n}]), {i, 0, Floor[(1/2) (-2 + u)]}], {k, 0, Floor[(1/2) (-1 + m)]}] + 2^(1 - m) E^(c u z) n! Sum[Binomial[m, k] Sum[(-1)^i Binomial[-1 + u, i] (E^((I a (-2 k + m) + c (-1 - 2 i + u)) z) Sum[(1/(-j + n)!) ((-1)^j (I a (-2 k + m) + c (-1 - 2 i + 2 u))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[h, 1], \[Ellipsis], Subscript[h, 1 + j], u}, {1 + Subscript[h, 1], \[Ellipsis], 1 + Subscript[h, 1 + j]}, -E^(2 c z)]), {j, 0, n}] + (-1)^(-1 + u) E^((I a (-2 k + m) - c (-1 - 2 i + u)) z) Sum[(1/(-j + n)!) ((-1)^j (c (1 + 2 i) + I a (-2 k + m))^ (-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[i, 1], \[Ellipsis], Subscript[i, 1 + j], u}, {1 + Subscript[i, 1], \[Ellipsis], 1 + Subscript[i, 1 + j]}, -E^(2 c z)]), {j, 0, n}]), {i, 0, Floor[(1/2) (-2 + u)]}], {k, 0, Floor[(1/2) (-1 + m)]}] /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == u/2 && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == (c u - I a (-2 k + m))/(2 c) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (c u + I a (-2 k + m))/(2 c) && Subscript[d, 1] == Subscript[d, 2] == \[Ellipsis] == Subscript[d, n + 1] == (-2 k + 2 u - 1)/2 && Subscript[e, 1] == Subscript[e, 2] == \[Ellipsis] == Subscript[e, n + 1] == (2 k + 1)/2 && Subscript[f, 1] == Subscript[f, 2] == \[Ellipsis] == Subscript[f, n + 1] == ((-I) a (-2 k + m) + c (-2 i + 2 u - 1))/(2 c) && Subscript[g, 1] == Subscript[g, 2] == \[Ellipsis] == Subscript[g, n + 1] == ((-I) a (-2 k + m) + c (2 i + 1))/(2 c) && Subscript[h, 1] == Subscript[h, 2] == \[Ellipsis] == Subscript[h, n + 1] == (I a (-2 k + m) + c (-2 i + 2 u - 1))/(2 c) && Subscript[i, 1] == Subscript[i, 2] == \[Ellipsis] == Subscript[i, n + 1] == (I a (-2 k + m) + c (2 i + 1))/(2 c) && Element[n, Integers] && n >= 0 && 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