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 FresnelC

 http://functions.wolfram.com/06.33.21.0018.01

 Input Form

 Integrate[z^3 E^(b z) FresnelC[a z], z] == ((1/(2 a^6 b^4 Pi^3)) (a b E^((I b^2)/(2 a^2 Pi) + b z) (I b^4 + a^2 b^2 Pi - 6 I a^4 Pi^2 - a^2 b^3 Pi z + 3 I a^4 b Pi^2 z - I a^4 b^2 Pi^2 z^2 + E^(I a^2 Pi z^2) ((-I) b^4 + 6 I a^4 Pi^2 - a^2 b^3 Pi z - 3 I a^4 b Pi^2 z + a^2 b^2 Pi (1 + I a^2 Pi z^2))) + E^((1/2) I a^2 Pi z^2) (2 a^6 E^((I b^2)/(2 a^2 Pi) + b z) Pi^3 (-6 + b z (6 + b z (-3 + b z))) FresnelC[a z] + E^((I b^2)/(a^2 Pi)) (b^6 - 3 a^4 b^2 Pi^2 - 6 I a^6 Pi^3) (FresnelC[b/(a Pi) + I a z] - I FresnelS[b/(a Pi) + I a z]) + ((-I) b^6 + 3 I a^4 b^2 Pi^2 + 6 a^6 Pi^3) (FresnelC[(I b)/(a Pi) + a z] - I FresnelS[(I b)/(a Pi) + 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 3 b z C TagBox["C", FresnelC] ( a z ) z 1 2 a 6 b 4 π 3 - ( π 2 z 2 a 4 + b 2 ) 2 a 2 π ( a b b 2 2 a 2 π + z b ( - 6 π 2 a 4 - b 2 π 2 z 2 a 4 + 3 b π 2 z a 4 - b 3 π z a 2 + b 2 π a 2 + b 4 + a 2 π z 2 ( 6 π 2 a 4 - 3 b π 2 z a 4 - b 3 π z a 2 + b 2 π ( a 2 π z 2 + 1 ) a 2 + b 4 ( - ) ) ) + 1 2 a 2 π z 2 ( 2 b 2 2 a 2 π + z b π 3 ( b z ( b z ( b z - 3 ) + 6 ) - 6 ) C TagBox["C", FresnelC] ( a z ) a 6 + ( 6 π 3 a 6 + 3 b 2 π 2 a 4 + b 6 ( - ) ) ( C TagBox["C", FresnelC] ( b a π + a z ) - S TagBox["S", FresnelS] ( b a π + a z ) ) + b 2 a 2 π ( - 6 π 3 a 6 - 3 b 2 π 2 a 4 + b 6 ) ( C TagBox["C", FresnelC] ( b a π + a z ) - S TagBox["S", FresnelS] ( b a π + a z ) ) ) ) z z 3 b z FresnelC a z 1 2 a 6 b 4 3 -1 -1 2 z 2 a 4 b 2 2 a 2 -1 a b b 2 2 a 2 -1 z b -6 2 a 4 -1 b 2 2 z 2 a 4 3 b 2 z a 4 -1 b 3 z a 2 b 2 a 2 b 4 a 2 z 2 6 2 a 4 -1 3 b 2 z a 4 -1 b 3 z a 2 b 2 a 2 z 2 1 a 2 b 4 -1 1 2 a 2 z 2 2 b 2 2 a 2 -1 z b 3 b z b z b z -3 6 -6 FresnelC a z a 6 6 3 a 6 3 b 2 2 a 4 b 6 -1 FresnelC b a -1 a z -1 FresnelS b a -1 a z b 2 a 2 -1 -6 3 a 6 -1 3 b 2 2 a 4 b 6 FresnelC b a -1 a z -1 FresnelS b a -1 a z [/itex]

 Rule Form

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

 2001-10-29