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 FresnelC

 http://functions.wolfram.com/06.33.21.0055.01

 Input Form

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