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 FresnelC

 http://functions.wolfram.com/06.33.21.0040.01

 Input Form

 Integrate[z Cos[b z] FresnelC[a z], z] == (1/b^2) ((1/(2 a^2 Pi)) (Cos[b^2/(2 a^2 Pi)] (a^2 Pi (FresnelC[b/(a Pi) - a z] - FresnelC[b/(a Pi) + a z]) + b^2 (-FresnelS[b/(a Pi) - a z] + FresnelS[b/(a Pi) + a z])) + (b^2 (FresnelC[b/(a Pi) - a z] - FresnelC[b/(a Pi) + a z]) + a^2 Pi (FresnelS[b/(a Pi) - a z] - FresnelS[b/(a Pi) + a z])) Sin[b^2/(2 a^2 Pi)]) + FresnelC[a z] (Cos[b z] + b z Sin[b z]) - (b Sin[b z] Sin[(1/2) a^2 Pi z^2])/(a Pi))

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29