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; }

 Sech

 http://functions.wolfram.com/01.24.21.0290.01

 Input Form

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