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 FresnelC

 http://functions.wolfram.com/06.33.21.0061.01

 Input Form

 Integrate[z^2 E^(b z) Cos[c z] FresnelC[a z], z] == ((1/(8 a^4 Pi^2)) (((1/(b + I c)^3) (2 I a (b + I c) E^((I (b + I c)^2)/(2 a^2 Pi) + (b + I c) z) (I (b + I c)^2 + 2 a^2 Pi - a^2 (b + I c) Pi z + E^(I a^2 Pi z^2) (I (b + I c)^2 - 2 a^2 Pi + a^2 (b + I c) Pi z)) + 2 E^((1/2) I a^2 Pi z^2) (2 a^4 E^((I (b + I c)^2)/(2 a^2 Pi) + (b + I c) z) Pi^2 (2 + (b + I c) z (-2 + b z + I c z)) FresnelC[a z] + E^((I (b + I c)^2)/(a^2 Pi)) (-(b + I c)^4 - I a^2 (b + I c)^2 Pi + 2 a^4 Pi^2) (I FresnelC[(b + I c)/(a Pi) + I a z] + FresnelS[(b + I c)/(a Pi) + I a z]) + ((b + I c)^4 - I a^2 (b + I c)^2 Pi - 2 a^4 Pi^2) (FresnelC[(I b - c)/(a Pi) + a z] - I FresnelS[(I b - c)/(a Pi) + a z]))))/ E^((I (b + I c)^2)/(2 a^2 Pi)) + ((1/(b - I c)^3) (2 I a (b - I c) E^(((b - I c) (I b + c + 2 a^2 Pi z))/ (2 a^2 Pi)) (I (b - I c)^2 + 2 a^2 Pi - a^2 (b - I c) Pi z + E^(I a^2 Pi z^2) (I (b - I c)^2 - 2 a^2 Pi + a^2 (b - I c) Pi z)) + 2 E^((1/2) I a^2 Pi z^2) (2 a^4 E^(((b - I c) (I b + c + 2 a^2 Pi z))/ (2 a^2 Pi)) Pi^2 (2 + (b - I c) z (-2 + b z - I c z)) FresnelC[a z] + E^((I (b - I c)^2)/(a^2 Pi)) (-(b - I c)^4 - I a^2 (b - I c)^2 Pi + 2 a^4 Pi^2) (I FresnelC[(b - I c)/(a Pi) + I a z] + FresnelS[(b - I c)/(a Pi) + I a z]) + ((b - I c)^4 - I a^2 (b - I c)^2 Pi - 2 a^4 Pi^2) (FresnelC[(I b + c + a^2 Pi z)/(a Pi)] - I FresnelS[(I b + c + a^2 Pi z)/(a Pi)]))))/ E^((I (b - I c)^2)/(2 a^2 Pi))))/E^((1/2) I a^2 Pi z^2)

 Standard Form

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 MathML Form

 z 2 b z cos ( c z ) C TagBox["C", FresnelC] ( a z ) z 1 8 a 4 π 2 - 1 2 a 2 π z 2 ( 1 ( b - c ) 3 - ( b - c ) 2 2 a 2 π ( 2 a ( b - c ) ( b - c ) ( 2 π z a 2 + c + b ) 2 a 2 π ( - ( b - c ) π z a 2 + 2 π a 2 + ( b - c ) 2 + a 2 π z 2 ( ( b - c ) π z a 2 - 2 π a 2 + ( b - c ) 2 ) ) + 2 1 2 a 2 π z 2 ( 2 ( b - c ) ( 2 π z a 2 + c + b ) 2 a 2 π π 2 ( ( b - c ) z ( b z - c z - 2 ) + 2 ) C TagBox["C", FresnelC] ( a z ) a 4 + ( - 2 π 2 a 4 - ( b - c ) 2 π a 2 + ( b - c ) 4 ) ( C TagBox["C", FresnelC] ( π z a 2 + c + b a π ) - S TagBox["S", FresnelS] ( π z a 2 + c + b a π ) ) + ( b - c ) 2 a 2 π ( 2 π 2 a 4 - ( b - c ) 2 π a 2 - ( b - c ) 4 ) ( C TagBox["C", FresnelC] ( b - c a π + a z ) + S TagBox["S", FresnelS] ( b - c a π + a z ) ) ) ) + 1 ( b + c ) 3 - ( b + c ) 2 2 a 2 π ( 2 a ( b + c ) ( b + c ) 2 2 a 2 π + z ( b + c ) ( - ( b + c ) π z a 2 + 2 π a 2 + ( b + c ) 2 + a 2 π z 2 ( ( b + c ) π z a 2 - 2 π a 2 + ( b + c ) 2 ) ) + 2 1 2 a 2 π z 2 ( 2 ( b + c ) 2 2 a 2 π + z ( b + c ) π 2 ( ( b + c ) z ( b z + c z - 2 ) + 2 ) C TagBox["C", FresnelC] ( a z ) a 4 + ( - 2 π 2 a 4 - ( b + c ) 2 π a 2 + ( b + c ) 4 ) ( C TagBox["C", FresnelC] ( b - c a π + a z ) - S TagBox["S", FresnelS] ( b - c a π + a z ) ) + ( b + c ) 2 a 2 π ( 2 π 2 a 4 - ( b + c ) 2 π a 2 - ( b + c ) 4 ) ( C TagBox["C", FresnelC] ( b + c a π + a z ) + S TagBox["S", FresnelS] ( b + c a π + a z ) ) ) ) ) z z 2 b z c z FresnelC a z 1 8 a 4 2 -1 -1 1 2 a 2 z 2 1 b -1 c 3 -1 -1 b -1 c 2 2 a 2 -1 2 a b -1 c b -1 c 2 z a 2 c b 2 a 2 -1 -1 b -1 c z a 2 2 a 2 b -1 c 2 a 2 z 2 b -1 c z a 2 -1 2 a 2 b -1 c 2 2 1 2 a 2 z 2 2 b -1 c 2 z a 2 c b 2 a 2 -1 2 b -1 c z b z -1 c z -2 2 FresnelC a z a 4 -2 2 a 4 -1 b -1 c 2 a 2 b -1 c 4 FresnelC z a 2 c b a -1 -1 FresnelS z a 2 c b a -1 b -1 c 2 a 2 -1 2 2 a 4 -1 b -1 c 2 a 2 -1 b -1 c 4 FresnelC b -1 c a -1 a z FresnelS b -1 c a -1 a z 1 b c 3 -1 -1 b c 2 2 a 2 -1 2 a b c b c 2 2 a 2 -1 z b c -1 b c z a 2 2 a 2 b c 2 a 2 z 2 b c z a 2 -1 2 a 2 b c 2 2 1 2 a 2 z 2 2 b c 2 2 a 2 -1 z b c 2 b c z b z c z -2 2 FresnelC a z a 4 -2 2 a 4 -1 b c 2 a 2 b c 4 FresnelC b -1 c a -1 a z -1 FresnelS b -1 c a -1 a z b c 2 a 2 -1 2 2 a 4 -1 b c 2 a 2 -1 b c 4 FresnelC b c a -1 a z FresnelS b c a -1 a z [/itex]

 Rule Form

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

 2001-10-29