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 FresnelC

 http://functions.wolfram.com/06.33.21.0125.01

 Input Form

 Integrate[z^2 Erfc[b z] FresnelC[a z], z] == (1/(12 Pi^2)) ((-(2/(a^3 b^3))) (((4 b^4 + I a^2 b^2 Pi - a^4 Pi^2)/Sqrt[-2 I b^2 + a^2 Pi]) (FresnelC[Sqrt[a^2 - (2 I b^2)/Pi] z] - I FresnelS[Sqrt[a^2 - (2 I b^2)/Pi] z]) + ((4 b^4 - I a^2 b^2 Pi - a^4 Pi^2)/Sqrt[2 I b^2 + a^2 Pi]) (FresnelC[Sqrt[a^2 + (2 I b^2)/Pi] z] + I FresnelS[Sqrt[a^2 + (2 I b^2)/Pi] z])) - (8 Cos[(1/2) a^2 Pi z^2] Erfc[b z])/a^3 + 4 Pi^(3/2) (-((1 + b^2 z^2)/(E^(b^2 z^2) b^3)) + Sqrt[Pi] z^3 Erfc[b z]) FresnelC[a z] + (4 Sqrt[Pi] z (Cosh[b^2 z^2] - b Sqrt[Pi] z Erfc[b z]) Sin[(1/2) a^2 Pi z^2])/(a b) - ((Sqrt[Pi] z)/(a b)) (I Sqrt[2 Pi] (1/Sqrt[(2 b^2 - I a^2 Pi) z^2] - 1/Sqrt[(2 b^2 + I a^2 Pi) z^2]) + 4 Sin[(1/2) a^2 Pi z^2] Sinh[b^2 z^2]))

 Standard Form

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 MathML Form

 z 2 erfc ( b z ) C TagBox["C", FresnelC] ( a z ) z 1 12 π 2 ( - 8 cos ( 1 2 a 2 π z 2 ) erfc ( b z ) a 3 + 4 π 3 / 2 ( π z 3 erfc ( b z ) - - b 2 z 2 ( b 2 z 2 + 1 ) b 3 ) C TagBox["C", FresnelC] ( a z ) - 2 a 3 b 3 ( - π 2 a 4 - b 2 π a 2 + 4 b 4 π a 2 + 2 b 2 ( C TagBox["C", FresnelC] ( a 2 + 2 b 2 π z ) + S TagBox["S", FresnelS] ( a 2 + 2 b 2 π z ) ) + - π 2 a 4 + b 2 π a 2 + 4 b 4 a 2 π - 2 b 2 ( C TagBox["C", FresnelC] ( a 2 - 2 b 2 π z ) - S TagBox["S", FresnelS] ( a 2 - 2 b 2 π z ) ) ) + 4 π z ( cosh ( b 2 z 2 ) - b π z erfc ( b z ) ) sin ( 1 2 a 2 π z 2 ) a b - π z a b ( 2 π ( 1 ( 2 b 2 - a 2 π ) z 2 - 1 ( π a 2 + 2 b 2 ) z 2 ) + 4 sin ( 1 2 a 2 π z 2 ) sinh ( b 2 z 2 ) ) ) z z 2 Erfc b z FresnelC a z 1 12 2 -1 -1 8 1 2 a 2 z 2 Erfc b z a 3 -1 4 3 2 1 2 z 3 Erfc b z -1 -1 b 2 z 2 b 2 z 2 1 b 3 -1 FresnelC a z -1 2 a 3 b 3 -1 -1 2 a 4 -1 b 2 a 2 4 b 4 a 2 2 b 2 1 2 -1 FresnelC a 2 2 b 2 -1 1 2 z FresnelS a 2 2 b 2 -1 1 2 z -1 2 a 4 b 2 a 2 4 b 4 a 2 -1 2 b 2 1 2 -1 FresnelC a 2 -1 2 b 2 -1 1 2 z -1 FresnelS a 2 -1 2 b 2 -1 1 2 z 4 1 2 z b 2 z 2 -1 b 1 2 z Erfc b z 1 2 a 2 z 2 a b -1 -1 1 2 z a b -1 2 1 2 1 2 b 2 -1 a 2 z 2 1 2 -1 -1 1 a 2 2 b 2 z 2 1 2 -1 4 1 2 a 2 z 2 b 2 z 2 [/itex]

 Rule Form

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

 2001-10-29