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/01.22.21.0232.01

 Input Form

 Integrate[z^n E^(p z) Cos[a z] Cosh[b z] Coth[c z], z] == (-(1/4)) n! (E^(((-I) a + b + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a + b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[v, 1], \[Ellipsis], Subscript[v, 1 + j], 1}, {1 + Subscript[v, 1], \[Ellipsis], 1 + Subscript[v, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^(((-I) a - b + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a - b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[t, 1], \[Ellipsis], Subscript[t, 1 + j], 1}, {1 + Subscript[t, 1], \[Ellipsis], 1 + Subscript[t, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^((I a - b + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a - b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[u, 1], \[Ellipsis], Subscript[u, 1 + j], 1}, {1 + Subscript[u, 1], \[Ellipsis], 1 + Subscript[u, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^((I a + b + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a + b + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[w, 1], \[Ellipsis], Subscript[w, 1 + j], 1}, {1 + Subscript[w, 1], \[Ellipsis], 1 + Subscript[w, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^(((-I) a - b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a - b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[x, 1], \[Ellipsis], Subscript[x, 1 + j], 1}, {1 + Subscript[x, 1], \[Ellipsis], 1 + Subscript[x, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^((I a - b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a - b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[y, 1], \[Ellipsis], Subscript[y, 1 + j], 1}, {1 + Subscript[y, 1], \[Ellipsis], 1 + Subscript[y, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^(((-I) a + b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j ((-I) a + b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[z, 1], \[Ellipsis], Subscript[z, 1 + j], 1}, {1 + Subscript[z, 1], \[Ellipsis], 1 + Subscript[z, 1 + j]}, E^(2 c z)]), {j, 0, n}] + E^((I a + b + 2 c + p) z) Sum[(1/(-j + n)!) ((-1)^j (I a + b + 2 c + p)^(-1 - j) z^(-j + n) HypergeometricPFQ[{Subscript[\[Alpha], 1], \[Ellipsis], Subscript[\[Alpha], 1 + j], 1}, {1 + Subscript[\[Alpha], 1], \[Ellipsis], 1 + Subscript[\[Alpha], 1 + j]}, E^(2 c z)]), {j, 0, n}]) /; Subscript[t, 1] == Subscript[t, 2] == \[Ellipsis] == Subscript[t, n + 1] == ((-I) a + p - b)/(2 c) && Subscript[u, 1] == Subscript[u, 2] == \[Ellipsis] == Subscript[u, n + 1] == (I a + p - b)/(2 c) && Subscript[v, 1] == Subscript[v, 2] == \[Ellipsis] == Subscript[v, n + 1] == ((-I) a + p + b)/(2 c) && Subscript[w, 1] == Subscript[w, 2] == \[Ellipsis] == Subscript[w, n + 1] == (I a + p + b)/(2 c) && Subscript[x, 1] == Subscript[x, 2] == \[Ellipsis] == Subscript[x, n + 1] == ((-I) a + p - b + 2 c)/(2 c) && Subscript[y, 1] == Subscript[y, 2] == \[Ellipsis] == Subscript[y, n + 1] == (I a + p - b + 2 c)/(2 c) && Subscript[z, 1] == Subscript[z, 2] == \[Ellipsis] == Subscript[z, n + 1] == ((-I) a + p + b + 2 c)/(2 c) && Subscript[\[Alpha], 1] == Subscript[\[Alpha], 2] == \[Ellipsis] == Subscript[\[Alpha], n + 1] == (I a + p + b + 2 c)/(2 c) && Element[n, Integers] && n >= 0

 Standard Form

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 MathML Form

 z n p z cos ( a z ) cosh ( b z ) coth ( c z ) z - 1 4 n ! 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 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2002-12-18