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 FresnelC

 http://functions.wolfram.com/06.33.21.0016.01

 Input Form

 Integrate[z E^(b z) FresnelC[a z], z] == ((1/(2 a^2 b^2 Pi)) (I a b E^((I b^2)/(2 a^2 Pi) + b z) (-1 + E^(I a^2 Pi z^2)) + E^((1/2) I a^2 Pi z^2) (2 a^2 E^((I b^2)/(2 a^2 Pi) + b z) Pi (-1 + b z) FresnelC[a z] - (b^2 - I a^2 Pi) (FresnelC[b/(a Pi) - I a z] + I FresnelS[b/(a Pi) - I a z]) - E^((I b^2)/(a^2 Pi)) (b^2 + I a^2 Pi) (FresnelC[b/(a Pi) + I a z] - I FresnelS[b/(a Pi) + I a z]))))/ E^((I (b^2 + a^4 Pi^2 z^2))/(2 a^2 Pi))

 Standard Form

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 MathML Form

 z b z C TagBox["C", FresnelC] ( a z ) z 1 2 a 2 b 2 π - ( π 2 z 2 a 4 + b 2 ) 2 a 2 π ( a b b 2 2 a 2 π + z b ( - 1 + a 2 π z 2 ) + 1 2 a 2 π z 2 ( 2 b 2 2 a 2 π + z b π ( b z - 1 ) C TagBox["C", FresnelC] ( a z ) a 2 - b 2 a 2 π ( π a 2 + b 2 ) ( C TagBox["C", FresnelC] ( b a π + a z ) - S TagBox["S", FresnelS] ( b a π + a z ) ) - ( b 2 - a 2 π ) ( C TagBox["C", FresnelC] ( b a π - a z ) + S TagBox["S", FresnelS] ( b a π - a z ) ) ) ) z z b z FresnelC a z 1 2 a 2 b 2 -1 -1 2 z 2 a 4 b 2 2 a 2 -1 a b b 2 2 a 2 -1 z b -1 a 2 z 2 1 2 a 2 z 2 2 b 2 2 a 2 -1 z b b z -1 FresnelC a z a 2 -1 b 2 a 2 -1 a 2 b 2 FresnelC b a -1 a z -1 FresnelS b a -1 a z -1 b 2 -1 a 2 FresnelC b a -1 -1 a z FresnelS b a -1 -1 a z [/itex]

 Rule Form

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

 2001-10-29