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 Cosh

 http://functions.wolfram.com/01.20.21.4861.01

 Input Form

 Integrate[E^(b z^2 + d z + e) Sin[a z^2 + p z + q] Sinh[w z^2 + s z + t] Cosh[c z^2 + f z + g]^v, z] == (-I) 2^(-3 - v) Binomial[v, v/2] (((-E^(e - I q - t - (d - I p - s)^2/(4 ((-I) a + b - w)))) (d - I p - s + 2 ((-I) a + b - w) z) Gamma[1/2, -((d - I p - s + 2 ((-I) a + b - w) z)^2/(4 ((-I) a + b - w)))])/ (((-I) a + b - w) Sqrt[-((d - I p - s + 2 ((-I) a + b - w) z)^2/ ((-I) a + b - w))]) + (E^(e + I q - t - (d + I p - s)^2/(4 (I a + b - w))) (d + I p - s + 2 (I a + b - w) z) Gamma[1/2, -((d + I p - s + 2 (I a + b - w) z)^2/(4 (I a + b - w)))])/ ((I a + b - w) Sqrt[-((d + I p - s + 2 (I a + b - w) z)^2/ (I a + b - w))]) + (E^(e - I q + t - (d - I p + s)^2/(4 ((-I) a + b + w))) (d - I p + s + 2 ((-I) a + b + w) z) Gamma[1/2, -((d - I p + s + 2 ((-I) a + b + w) z)^2/(4 ((-I) a + b + w)))])/ (((-I) a + b + w) Sqrt[-((d - I p + s + 2 ((-I) a + b + w) z)^2/ ((-I) a + b + w))]) - (E^(e + I q + t - (d + I p + s)^2/(4 (I a + b + w))) (d + I p + s + 2 (I a + b + w) z) Gamma[1/2, -((d + I p + s + 2 (I a + b + w) z)^2/(4 (I a + b + w)))])/ ((I a + b + w) Sqrt[-((d + I p + s + 2 (I a + b + w) z)^2/ (I a + b + w))])) (1 - Mod[v, 2]) - I 2^(-3 - v) Sum[Binomial[v, h] (((-E^(e - I q - t + g (2 h - v) - (d - I p - s + f (2 h - v))^2/ (4 ((-I) a + b + c (2 h - v) - w)))) (d - I p - s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) - w) z) Gamma[1/2, -((d - I p - s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) - w) z)^2/(4 ((-I) a + b + c (2 h - v) - w)))])/ (((-I) a + b + c (2 h - v) - w) Sqrt[-((d - I p - s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) - w) z)^2/((-I) a + b + c (2 h - v) - w))]) + (E^(e + I q - t + g (2 h - v) - (d + I p - s + f (2 h - v))^2/ (4 (I a + b + c (2 h - v) - w))) (d + I p - s + f (2 h - v) + 2 (I a + b + c (2 h - v) - w) z) Gamma[1/2, -((d + I p - s + f (2 h - v) + 2 (I a + b + c (2 h - v) - w) z)^2/ (4 (I a + b + c (2 h - v) - w)))])/((I a + b + c (2 h - v) - w) Sqrt[-((d + I p - s + f (2 h - v) + 2 (I a + b + c (2 h - v) - w) z)^ 2/(I a + b + c (2 h - v) - w))]) - (E^(e - I q - t + g (-2 h + v) - (d - I p - s + f (-2 h + v))^2/ (4 ((-I) a + b + c (-2 h + v) - w))) (d - I p - s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) - w) z) Gamma[1/2, -((d - I p - s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) - w) z)^2/(4 ((-I) a + b + c (-2 h + v) - w)))])/ (((-I) a + b + c (-2 h + v) - w) Sqrt[-((d - I p - s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) - w) z)^2/((-I) a + b + c (-2 h + v) - w))]) + (E^(e + I q - t + g (-2 h + v) - (d + I p - s + f (-2 h + v))^2/ (4 (I a + b + c (-2 h + v) - w))) (d + I p - s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) - w) z) Gamma[1/2, -((d + I p - s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) - w) z)^2/ (4 (I a + b + c (-2 h + v) - w)))])/((I a + b + c (-2 h + v) - w) Sqrt[-((d + I p - s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) - w) z)^2/(I a + b + c (-2 h + v) - w))]) + (E^(e - I q + t + g (2 h - v) - (d - I p + s + f (2 h - v))^2/ (4 ((-I) a + b + c (2 h - v) + w))) (d - I p + s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) + w) z) Gamma[1/2, -((d - I p + s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) + w) z)^ 2/(4 ((-I) a + b + c (2 h - v) + w)))])/ (((-I) a + b + c (2 h - v) + w) Sqrt[-((d - I p + s + f (2 h - v) + 2 ((-I) a + b + c (2 h - v) + w) z)^2/((-I) a + b + c (2 h - v) + w))]) - (E^(e + I q + t + g (2 h - v) - (d + I p + s + f (2 h - v))^2/ (4 (I a + b + c (2 h - v) + w))) (d + I p + s + f (2 h - v) + 2 (I a + b + c (2 h - v) + w) z) Gamma[1/2, -((d + I p + s + f (2 h - v) + 2 (I a + b + c (2 h - v) + w) z)^2/ (4 (I a + b + c (2 h - v) + w)))])/((I a + b + c (2 h - v) + w) Sqrt[-((d + I p + s + f (2 h - v) + 2 (I a + b + c (2 h - v) + w) z)^ 2/(I a + b + c (2 h - v) + w))]) + (E^(e - I q + t + g (-2 h + v) - (d - I p + s + f (-2 h + v))^2/ (4 ((-I) a + b + c (-2 h + v) + w))) (d - I p + s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) + w) z) Gamma[1/2, -((d - I p + s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) + w) z)^2/(4 ((-I) a + b + c (-2 h + v) + w)))])/ (((-I) a + b + c (-2 h + v) + w) Sqrt[-((d - I p + s + f (-2 h + v) + 2 ((-I) a + b + c (-2 h + v) + w) z)^2/((-I) a + b + c (-2 h + v) + w))]) - (E^(e + I q + t + g (-2 h + v) - (d + I p + s + f (-2 h + v))^2/ (4 (I a + b + c (-2 h + v) + w))) (d + I p + s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) + w) z) Gamma[1/2, -((d + I p + s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) + w) z)^2/ (4 (I a + b + c (-2 h + v) + w)))])/((I a + b + c (-2 h + v) + w) Sqrt[-((d + I p + s + f (-2 h + v) + 2 (I a + b + c (-2 h + v) + w) z)^2/(I a + b + c (-2 h + v) + w))])), {h, 0, Floor[(1/2) (-1 + v)]}] /; Element[v, Integers] && v > 0

 Standard Form

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 MathML Form

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v + Condition z b z 2 d z e a z 2 p z q w z 2 s z t c z 2 f z g v -1 2 -1 v -3 -1 -1 d -1 p -1 s 2 4 b -1 a -1 w -1 e -1 q -1 t d -1 p -1 s 2 b -1 a -1 w z Gamma 1 2 -1 d -1 p -1 s 2 b -1 a -1 w z 2 4 b -1 a -1 w -1 b -1 a -1 w -1 d -1 p -1 s 2 b -1 a -1 w z 2 b -1 a -1 w -1 1 2 -1 -1 d p -1 s 2 4 b a -1 w -1 e q -1 t d p -1 s 2 b a -1 w z Gamma 1 2 -1 d p -1 s 2 b a -1 w z 2 4 b a -1 w -1 b a -1 w -1 d p -1 s 2 b a -1 w z 2 b a -1 w -1 1 2 -1 -1 d -1 p s 2 4 b -1 a w -1 e -1 q t d -1 p s 2 b -1 a w z Gamma 1 2 -1 d -1 p s 2 b -1 a w z 2 4 b -1 a w -1 b -1 a w -1 d -1 p s 2 b -1 a w z 2 b -1 a w -1 1 2 -1 -1 -1 d p s 2 4 b a w -1 e q t d p s 2 b a w z Gamma 1 2 -1 d p s 2 b a w z 2 4 b a w -1 b a w -1 d p s 2 b a w z 2 b a w -1 1 2 -1 Binomial v v 2 -1 1 -1 \$CellContext`v 2 -1 2 -1 v -3 h 0 v -1 2 -1 Binomial v h -1 -1 d -1 p -1 s f 2 h -1 v 2 4 b -1 a c 2 h -1 v -1 w -1 e -1 q -1 t g 2 h -1 v d -1 p -1 s f 2 h -1 v 2 b -1 a c 2 h -1 v -1 w z Gamma 1 2 -1 d -1 p -1 s f 2 h -1 v 2 b -1 a c 2 h -1 v -1 w z 2 4 b -1 a c 2 h -1 v -1 w -1 b -1 a c 2 h -1 v -1 w -1 d -1 p -1 s f 2 h -1 v 2 b -1 a c 2 h -1 v -1 w z 2 b -1 a c 2 h -1 v -1 w -1 1 2 -1 -1 d p -1 s f 2 h -1 v 2 4 b a c 2 h -1 v -1 w -1 e q -1 t g 2 h -1 v d p -1 s f 2 h -1 v 2 b a c 2 h -1 v -1 w z Gamma 1 2 -1 d p -1 s f 2 h -1 v 2 b a c 2 h -1 v -1 w z 2 4 b a c 2 h -1 v -1 w -1 b a c 2 h -1 v -1 w -1 d p -1 s f 2 h -1 v 2 b a c 2 h -1 v -1 w z 2 b a c 2 h -1 v -1 w -1 1 2 -1 -1 -1 d -1 p -1 s f v -1 2 h 2 4 b -1 a c v -1 2 h -1 w -1 e -1 q -1 t g v -1 2 h d -1 p -1 s f v -1 2 h 2 b -1 a c v -1 2 h -1 w z Gamma 1 2 -1 d -1 p -1 s f v -1 2 h 2 b -1 a c v -1 2 h -1 w z 2 4 b -1 a c v -1 2 h -1 w -1 b -1 a c v -1 2 h -1 w -1 d -1 p -1 s f v -1 2 h 2 b -1 a c v -1 2 h -1 w z 2 b -1 a c v -1 2 h -1 w -1 1 2 -1 -1 d p -1 s f v -1 2 h 2 4 b a c v -1 2 h -1 w -1 e q -1 t g v -1 2 h d p -1 s f v -1 2 h 2 b a c v -1 2 h -1 w z Gamma 1 2 -1 d p -1 s f v -1 2 h 2 b a c v -1 2 h -1 w z 2 4 b a c v -1 2 h -1 w -1 b a c v -1 2 h -1 w -1 d p -1 s f v -1 2 h 2 b a c v -1 2 h -1 w z 2 b a c v -1 2 h -1 w -1 1 2 -1 -1 d -1 p s f 2 h -1 v 2 4 b -1 a c 2 h -1 v w -1 e -1 q t g 2 h -1 v d -1 p s f 2 h -1 v 2 b -1 a c 2 h -1 v w z Gamma 1 2 -1 d -1 p s f 2 h -1 v 2 b -1 a c 2 h -1 v w z 2 4 b -1 a c 2 h -1 v w -1 b -1 a c 2 h -1 v w -1 d -1 p s f 2 h -1 v 2 b -1 a c 2 h -1 v w z 2 b -1 a c 2 h -1 v w -1 1 2 -1 -1 -1 d p s f 2 h -1 v 2 4 b a c 2 h -1 v w -1 e q t g 2 h -1 v d p s f 2 h -1 v 2 b a c 2 h -1 v w z Gamma 1 2 -1 d p s f 2 h -1 v 2 b a c 2 h -1 v w z 2 4 b a c 2 h -1 v w -1 b a c 2 h -1 v w -1 d p s f 2 h -1 v 2 b a c 2 h -1 v w z 2 b a c 2 h -1 v w -1 1 2 -1 -1 d -1 p s f v -1 2 h 2 4 b -1 a c v -1 2 h w -1 e -1 q t g v -1 2 h d -1 p s f v -1 2 h 2 b -1 a c v -1 2 h w z Gamma 1 2 -1 d -1 p s f v -1 2 h 2 b -1 a c v -1 2 h w z 2 4 b -1 a c v -1 2 h w -1 b -1 a c v -1 2 h w -1 d -1 p s f v -1 2 h 2 b -1 a c v -1 2 h w z 2 b -1 a c v -1 2 h w -1 1 2 -1 -1 -1 d p s f v -1 2 h 2 4 b a c v -1 2 h w -1 e q t g v -1 2 h d p s f v -1 2 h 2 b a c v -1 2 h w z Gamma 1 2 -1 d p s f v -1 2 h 2 b a c v -1 2 h w z 2 4 b a c v -1 2 h w -1 b a c v -1 2 h w -1 d p s f v -1 2 h 2 b a c v -1 2 h w z 2 b a c v -1 2 h w -1 1 2 -1 v SuperPlus [/itex]

 Rule Form

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

 2002-12-18