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/01.22.21.0231.01

 Input Form

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