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 FresnelC

 http://functions.wolfram.com/06.33.21.0049.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29