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/01.23.21.0280.01

 Input Form

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