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/01.22.21.0229.01

 Input Form

 Integrate[z^n E^(p z) Sin[a z] Cosh[c z] Coth[c z], z] == (-(1/2)) I E^(c z) n! ((-E^((I a + p) z)) Sum[(1/(-j + n)!) ((-1)^j (I a + 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}] + E^(((-I) a + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a + c + 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}]) - (1/4) I E^(c z) n! ((-E^((I a - 2 c + p) z)) Sum[(1/(-j + n)!) ((-1)^j (I a - c + 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}] + E^(((-I) a - 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a - c + p)^(-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^((I a + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a + 3 c + p)^(-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}] + E^(((-I) a + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a + 3 c + p)^(-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}]) /; Subscript[a, 1] == Subscript[a, 2] == \[Ellipsis] == Subscript[a, n + 1] == (c + p + I a)/(2 c) && Subscript[b, 1] == Subscript[b, 2] == \[Ellipsis] == Subscript[b, n + 1] == (c + p - I a)/(2 c) && Subscript[c, 1] == Subscript[c, 2] == \[Ellipsis] == Subscript[c, n + 1] == (p + I a - c)/(2 c) && Subscript[d, 1] == Subscript[d, 2] == \[Ellipsis] == Subscript[d, n + 1] == (p - I a - c)/(2 c) && Subscript[e, 1] == Subscript[e, 2] == \[Ellipsis] == Subscript[e, n + 1] == (p + I a + 3 c)/(2 c) && Subscript[f, 1] == Subscript[f, 2] == \[Ellipsis] == Subscript[f, n + 1] == (p - I a + 3 c)/(2 c) && Element[n, Integers] && n >= 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