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 FresnelC

 http://functions.wolfram.com/06.33.21.0127.01

 Input Form

 Integrate[z^2 Erfi[b z] FresnelC[a z], z] == (1/(12 Pi^2)) (((4 Pi^(3/2))/b^3) (E^(b^2 z^2) (1 - b^2 z^2) + b^3 Sqrt[Pi] z^3 Erfi[b z]) FresnelC[a z] + (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])) + (4 Sqrt[Pi] z Cosh[b^2 z^2] Sin[(1/2) a^2 Pi z^2])/(a b) - (4 Erfi[b z] (2 Cos[(1/2) a^2 Pi z^2] + a^2 Pi z^2 Sin[(1/2) a^2 Pi z^2]))/ a^3 - ((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 erfi ( b z ) C TagBox["C", FresnelC] ( a z ) z 1 12 π 2 ( ( 4 π 3 / 2 ) ( b 3 π erfi ( b z ) z 3 + b 2 z 2 ( 1 - b 2 z 2 ) ) C TagBox["C", FresnelC] ( a z ) b 3 + 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 ) sin ( 1 2 a 2 π z 2 ) a b - π z a b ( 2 π ( 1 - ( π a 2 + 2 b 2 ) z 2 - 1 ( a 2 π - 2 b 2 ) z 2 ) - 4 sin ( 1 2 a 2 π z 2 ) sinh ( b 2 z 2 ) ) - 4 erfi ( b z ) ( a 2 π sin ( 1 2 a 2 π z 2 ) z 2 + 2 cos ( 1 2 a 2 π z 2 ) ) a 3 ) z z 2 Erfi b z FresnelC a z 1 12 2 -1 4 3 2 b 3 1 2 Erfi b z z 3 b 2 z 2 1 -1 b 2 z 2 FresnelC a z b 3 -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 -1 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 FresnelS a 2 -1 2 b 2 -1 1 2 z 4 1 2 z b 2 z 2 1 2 a 2 z 2 a b -1 -1 1 2 z a b -1 2 1 2 1 -1 a 2 2 b 2 z 2 1 2 -1 -1 1 a 2 -1 2 b 2 z 2 1 2 -1 -1 4 1 2 a 2 z 2 b 2 z 2 -1 4 Erfi b z a 2 1 2 a 2 z 2 z 2 2 1 2 a 2 z 2 a 3 -1 [/itex]

 Rule Form

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

 2001-10-29