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 FresnelC

 http://functions.wolfram.com/06.33.21.0081.01

 Input Form

 Integrate[z^3 Cosh[b z] FresnelC[a z], z] == (1/(2 a^6 b^4 Pi^3)) ((-FresnelS[(I b)/(a Pi) - a z] + FresnelS[(I b)/(a Pi) + a z]) ((-b^2) (b^4 - 3 a^4 Pi^2) Cos[b^2/(2 a^2 Pi)] - 6 a^6 Pi^3 Sin[b^2/(2 a^2 Pi)]) + FresnelC[(I b)/(a Pi) + a z] (6 a^6 Pi^3 Cos[b^2/(2 a^2 Pi)] - b^2 (b^4 - 3 a^4 Pi^2) Sin[b^2/(2 a^2 Pi)]) + FresnelC[(I b)/(a Pi) - a z] (-6 a^6 Pi^3 Cos[b^2/(2 a^2 Pi)] + b^2 (b^4 - 3 a^4 Pi^2) Sin[b^2/(2 a^2 Pi)]) - 2 a^3 b^3 Pi Cos[(1/2) a^2 Pi z^2] (b z Cosh[b z] - Sinh[b z]) + 2 a^6 Pi^3 FresnelC[a z] (-3 (2 + b^2 z^2) Cosh[b z] + b z (6 + b^2 z^2) Sinh[b z]) - 2 a b Sin[(1/2) a^2 Pi z^2] (-3 a^4 b Pi^2 z Cosh[b z] + (-b^4 + 6 a^4 Pi^2 + a^4 b^2 Pi^2 z^2) Sinh[b z]))

 Standard Form

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 MathML Form

 z 3 cosh ( b z ) C TagBox["C", FresnelC] ( a z ) z 1 2 a 6 b 4 π 3 ( 2 π 3 C TagBox["C", FresnelC] ( a z ) ( b z ( b 2 z 2 + 6 ) sinh ( b z ) - 3 ( b 2 z 2 + 2 ) cosh ( b z ) ) a 6 - 2 b 3 π cos ( 1 2 a 2 π z 2 ) ( b z cosh ( b z ) - sinh ( b z ) ) a 3 - 2 b sin ( 1 2 a 2 π z 2 ) ( ( 6 π 2 a 4 + b 2 π 2 z 2 a 4 - b 4 ) sinh ( b z ) - 3 a 4 b π 2 z cosh ( b z ) ) a + C TagBox["C", FresnelC] ( b a π - a z ) ( b 2 ( b 4 - 3 a 4 π 2 ) sin ( b 2 2 a 2 π ) - 6 a 6 π 3 cos ( b 2 2 a 2 π ) ) + ( S TagBox["S", FresnelS] ( b a π + a z ) - S TagBox["S", FresnelS] ( b a π - a z ) ) ( - 6 π 3 sin ( b 2 2 a 2 π ) a 6 - b 2 ( b 4 - 3 a 4 π 2 ) cos ( b 2 2 a 2 π ) ) + C TagBox["C", FresnelC] ( b a π + a z ) ( 6 a 6 π 3 cos ( b 2 2 a 2 π ) - b 2 ( b 4 - 3 a 4 π 2 ) sin ( b 2 2 a 2 π ) ) ) z z 3 b z FresnelC a z 1 2 a 6 b 4 3 -1 2 3 FresnelC a z b z b 2 z 2 6 b z -1 3 b 2 z 2 2 b z a 6 -1 2 b 3 1 2 a 2 z 2 b z b z -1 b z a 3 -1 2 b 1 2 a 2 z 2 6 2 a 4 b 2 2 z 2 a 4 -1 b 4 b z -1 3 a 4 b 2 z b z a FresnelC b a -1 -1 a z b 2 b 4 -1 3 a 4 2 b 2 2 a 2 -1 -1 6 a 6 3 b 2 2 a 2 -1 FresnelS b a -1 a z -1 FresnelS b a -1 -1 a z -6 3 b 2 2 a 2 -1 a 6 -1 b 2 b 4 -1 3 a 4 2 b 2 2 a 2 -1 FresnelC b a -1 a z 6 a 6 3 b 2 2 a 2 -1 -1 b 2 b 4 -1 3 a 4 2 b 2 2 a 2 -1 [/itex]

 Rule Form

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

 2001-10-29