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 FresnelC

 http://functions.wolfram.com/06.33.21.0053.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29