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 FresnelC

 http://functions.wolfram.com/06.33.21.0060.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29