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 FresnelC

 http://functions.wolfram.com/06.33.21.0045.01

 Input Form

 Integrate[z^3 Cos[b z^2] FresnelC[a z], z] == (1/(32 b^2)) (2 I a Sqrt[2 Pi] (((3 b + a^2 Pi) Erfi[Sqrt[(-I) b - (1/2) I a^2 Pi] z])/ ((-I) (2 b + a^2 Pi))^(3/2) + ((-3 b + a^2 Pi) Erfi[Sqrt[I b - (1/2) I a^2 Pi] z])/ ((-I) (-2 b + a^2 Pi))^(3/2) - ((-3 b + a^2 Pi) Erfi[Sqrt[(-I) b + (1/2) I a^2 Pi] z])/ (I (-2 b + a^2 Pi))^(3/2) - ((3 b + a^2 Pi) Erfi[Sqrt[I b + (1/2) I a^2 Pi] z])/ (I (2 b + a^2 Pi))^(3/2)) + 16 FresnelC[a z] (Cos[b z^2] + b z^2 Sin[b z^2]) - ((16 a b z)/(-4 b^2 + a^4 Pi^2)) (2 b Cos[b z^2] Cos[(1/2) a^2 Pi z^2] + a^2 Pi Sin[b z^2] Sin[(1/2) a^2 Pi z^2]))

 Standard Form

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 MathML Form

 z 3 cos ( b z 2 ) C TagBox["C", FresnelC] ( a z ) z 1 32 b 2 ( 2 a 2 π ( - ( a 2 π - 3 b ) erfi ( 1 2 a 2 π - b z ) ( ( a 2 π - 2 b ) ) 3 / 2 + ( π a 2 + 3 b ) erfi ( - 1 2 π a 2 + b ( - ) z ) ( - ( π a 2 + 2 b ) ) 3 / 2 + ( a 2 π - 3 b ) erfi ( b - 1 2 a 2 π z ) ( - ( a 2 π - 2 b ) ) 3 / 2 - ( π a 2 + 3 b ) erfi ( 1 2 π a 2 + b z ) ( ( π a 2 + 2 b ) ) 3 / 2 ) + 16 C TagBox["C", FresnelC] ( a z ) ( b sin ( b z 2 ) z 2 + cos ( b z 2 ) ) - 16 a b z a 4 π 2 - 4 b 2 ( π sin ( b z 2 ) sin ( 1 2 a 2 π z 2 ) a 2 + 2 b cos ( b z 2 ) cos ( 1 2 a 2 π z 2 ) ) ) z z 3 b z 2 FresnelC a z 1 32 b 2 -1 2 a 2 1 2 -1 a 2 -1 3 b Erfi 1 2 a 2 -1 b 1 2 z a 2 -1 2 b 3 2 -1 a 2 3 b Erfi -1 1 2 a 2 b -1 1 2 z -1 a 2 2 b 3 2 -1 a 2 -1 3 b Erfi b -1 1 2 a 2 1 2 z -1 a 2 -1 2 b 3 2 -1 -1 a 2 3 b Erfi 1 2 a 2 b 1 2 z a 2 2 b 3 2 -1 16 FresnelC a z b b z 2 z 2 b z 2 -1 16 a b z a 4 2 -1 4 b 2 -1 b z 2 1 2 a 2 z 2 a 2 2 b b z 2 1 2 a 2 z 2 [/itex]

 Rule Form

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

 2001-10-29