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 FresnelC

 http://functions.wolfram.com/06.33.21.0020.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29