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/01.23.21.0255.01

 Input Form

 Integrate[E^(p z) Cos[a z]^m Cosh[b z]^u Csch[c z], z] == (-(1/(c + p))) 2^(1 - m - u) E^((c + p) z) Binomial[m, m/2] Binomial[u, u/2] (-1 + Mod[m, 2]) (-1 + Mod[u, 2]) HypergeometricPFQ[{(p + c)/(2 c), 1}, {1 + (p + c)/(2 c)}, E^(2 c z)] + 2^(1 - m - u) E^(c z) Binomial[u, u/2] (-1 + Mod[u, 2]) Sum[Binomial[m, s] ((E^((p + I a (m - 2 s)) z) HypergeometricPFQ[ {(I a (m - 2 s) + p + c)/(2 c), 1}, {1 + (I a (m - 2 s) + p + c)/(2 c)}, E^(2 c z)])/ (p + I a (m - 2 s) + c) + (E^((p - I a (m - 2 s)) z) HypergeometricPFQ[{((-I) a (m - 2 s) + p + c)/(2 c), 1}, {((-I) a (m - 2 s) + p + c)/(2 c) + 1}, E^(2 c z)])/ (p - I a (m - 2 s) + c)), {s, 0, Floor[(1/2) (-1 + m)]}] + 2^(1 - m - u) E^(c z) Binomial[m, m/2] (-1 + Mod[m, 2]) Sum[Binomial[u, k] (E^((p - b (-2 k + u)) z) (HypergeometricPFQ[{((-b) (u - 2 k) + p + c)/(2 c), 1}, {1 + ((-b) (u - 2 k) + p + c)/(2 c)}, E^(2 c z)]/ (p - b (-2 k + u) + c)) + E^((p + b (-2 k + u)) z) (HypergeometricPFQ[{(b (u - 2 k) + p + c)/(2 c), 1}, {1 + (b (u - 2 k) + p + c)/(2 c)}, E^(2 c z)]/(p + b (-2 k + u) + c))), {k, 0, Floor[(1/2) (-1 + u)]}] - 2^(1 - m - u) E^(c z) Sum[Binomial[m, s] Binomial[u, k] (E^((p + I a (m - 2 s) - b (-2 k + u)) z) (HypergeometricPFQ[{(I a (m - 2 s) - b (u - 2 k) + p + c)/(2 c), 1}, {1 + (I a (m - 2 s) - b (u - 2 k) + p + c)/(2 c)}, E^(2 c z)]/ (p + I a (m - 2 s) - b (-2 k + u) + c)) + E^((p - I a (m - 2 s) - b (-2 k + u)) z) (HypergeometricPFQ[{(p - I a (m - 2 s) - b (-2 k + u) + c)/(2 c), 1}, {1 + (p - I a (m - 2 s) - b (-2 k + u) + c)/(2 c)}, E^(2 c z)]/ (p - I a (m - 2 s) - b (-2 k + u) + c)) + E^((p + I a (m - 2 s) + b (-2 k + u)) z) (HypergeometricPFQ[{(p + I a (m - 2 s) + b (-2 k + u) + c)/(2 c), 1}, {1 + (p + I a (m - 2 s) + b (-2 k + u) + c)/(2 c)}, E^(2 c z)]/ (p + I a (m - 2 s) + b (-2 k + u) + c)) + E^((p - I a (m - 2 s) + b (-2 k + u)) z) (HypergeometricPFQ[{(p - I a (m - 2 s) + b (-2 k + u) + c)/(2 c), 1}, {1 + (p - I a (m - 2 s) + b (-2 k + u) + c)/(2 c)}, E^(2 c z)]/ (p - I a (m - 2 s) + b (-2 k + u) + c))), {k, 0, Floor[(1/2) (-1 + u)]}, {s, 0, Floor[(1/2) (-1 + m)]}] /; Element[m, Integers] && m > 0 && Element[u, Integers] && u > 0

 Standard Form

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 MathML Form

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m + u + Condition z p z a z m b z u c z -1 2 -1 m -1 u 1 c p z c p -1 Binomial m m 2 -1 Binomial u u 2 -1 \$CellContext`m 2 -1 \$CellContext`u 2 -1 HypergeometricPFQ c p 2 c -1 1 c p 2 c -1 1 2 c z 2 -1 m -1 u 1 c z Binomial u u 2 -1 \$CellContext`u 2 -1 s 0 m -1 2 -1 Binomial m s p -1 a m -1 2 s z c p -1 a m -1 2 s -1 HypergeometricPFQ c p -1 a m -1 2 s 2 c -1 1 c p -1 a m -1 2 s 2 c -1 1 2 c z p a m -1 2 s z c p a m -1 2 s -1 HypergeometricPFQ c p a m -1 2 s 2 c -1 1 c p a m -1 2 s 2 c -1 1 2 c z 2 -1 m -1 u 1 c z Binomial m m 2 -1 \$CellContext`m 2 -1 k 0 u -1 2 -1 Binomial u k p b u -1 2 k z c p b u -1 2 k -1 HypergeometricPFQ c b u -1 2 k p 2 c -1 1 c b u -1 2 k p 2 c -1 1 2 c z p -1 b u -1 2 k z c p -1 b u -1 2 k -1 HypergeometricPFQ c -1 b u -1 2 k p 2 c -1 1 c -1 b u -1 2 k p 2 c -1 1 2 c z -1 2 -1 m -1 u 1 c z s 0 m -1 2 -1 k 0 u -1 2 -1 Binomial m s Binomial u k p a m -1 2 s b u -1 2 k z c p a m -1 2 s b u -1 2 k -1 HypergeometricPFQ c p a m -1 2 s b u -1 2 k 2 c -1 1 c p a m -1 2 s b u -1 2 k 2 c -1 1 2 c z p -1 a m -1 2 s b u -1 2 k z c p -1 a m -1 2 s b u -1 2 k -1 HypergeometricPFQ c p -1 a m -1 2 s b u -1 2 k 2 c -1 1 c p -1 a m -1 2 s b u -1 2 k 2 c -1 1 2 c z p a m -1 2 s -1 b u -1 2 k z c p a m -1 2 s -1 b u -1 2 k -1 HypergeometricPFQ c -1 b u -1 2 k p a m -1 2 s 2 c -1 1 c -1 b u -1 2 k p a m -1 2 s 2 c -1 1 2 c z p -1 a m -1 2 s -1 b u -1 2 k z c p -1 a m -1 2 s -1 b u -1 2 k -1 HypergeometricPFQ c p -1 a m -1 2 s -1 b u -1 2 k 2 c -1 1 c p -1 a m -1 2 s -1 b u -1 2 k 2 c -1 1 2 c z m SuperPlus u SuperPlus [/itex]

 Rule Form

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

 2002-12-18

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