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 FresnelC

 http://functions.wolfram.com/06.33.21.0057.01

 Input Form

 Integrate[z E^(b z^2) Sin[c z^2] FresnelC[a z], z] == (1/16) (a Sqrt[2 Pi] z (I/((b - I c) Sqrt[(-2 b + 2 I c - I a^2 Pi) z^2]) - I/((b + I c) Sqrt[I (2 I b - 2 c + a^2 Pi) z^2]) + I/((b - I c) Sqrt[I (2 I b + 2 c + a^2 Pi) z^2]) - I/((b + I c) Sqrt[(-(2 b + I (2 c + a^2 Pi))) z^2]) + ((1 - I) FresnelC[((1 - I) Sqrt[I (2 I b + 2 c + a^2 Pi) z^2])/ Sqrt[2 Pi]])/((b - I c) Sqrt[I (2 I b + 2 c + a^2 Pi) z^2]) - ((1 - I) FresnelC[((1 - I) Sqrt[(-(b + I (c - (a^2 Pi)/2))) z^2])/ Sqrt[Pi]])/((b + I c) Sqrt[I (2 I b - 2 c + a^2 Pi) z^2]) - ((1 - I) FresnelC[((1 - I) Sqrt[(-(b + I (c + (a^2 Pi)/2))) z^2])/ Sqrt[Pi]])/((b + I c) Sqrt[(-(2 b + I (2 c + a^2 Pi))) z^2]) + ((1 - I) FresnelC[((1 - I) Sqrt[(-(b + (1/2) I (-2 c + a^2 Pi))) z^2])/ Sqrt[Pi]])/((b - I c) Sqrt[(-2 b + 2 I c - I a^2 Pi) z^2]) - ((1 + I) FresnelS[((1 - I) Sqrt[I (2 I b + 2 c + a^2 Pi) z^2])/ Sqrt[2 Pi]])/((b - I c) Sqrt[I (2 I b + 2 c + a^2 Pi) z^2]) + ((1 + I) FresnelS[((1 - I) Sqrt[(-(b + I (c - (a^2 Pi)/2))) z^2])/ Sqrt[Pi]])/((b + I c) Sqrt[I (2 I b - 2 c + a^2 Pi) z^2]) + ((1 + I) FresnelS[((1 - I) Sqrt[(-(b + I (c + (a^2 Pi)/2))) z^2])/ Sqrt[Pi]])/((b + I c) Sqrt[(-(2 b + I (2 c + a^2 Pi))) z^2]) - ((1 + I) FresnelS[((1 - I) Sqrt[(-(b + (1/2) I (-2 c + a^2 Pi))) z^2])/ Sqrt[Pi]])/((b - I c) Sqrt[(-2 b + 2 I c - I a^2 Pi) z^2])) + (8 E^(b z^2) FresnelC[a z] ((-c) Cos[c z^2] + b Sin[c z^2]))/(b^2 + c^2))

 Standard Form

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 MathML Form

 z b z 2 sin ( c z 2 ) C TagBox["C", FresnelC] ( a z ) z 1 16 ( a 2 π z ( ( b - c ) ( - π a 2 - 2 b + 2 c ) z 2 - ( b + c ) ( π a 2 - 2 c + 2 b ) z 2 + ( b - c ) ( π a 2 + 2 c + 2 b ) z 2 - ( b + c ) - ( 2 b + ( π a 2 + 2 c ) ) z 2 + ( 1 - ) C TagBox["C", FresnelC] ( ( 1 - ) ( π a 2 + 2 c + 2 b ) z 2 2 π ) ( b - c ) ( π a 2 + 2 c + 2 b ) z 2 - ( 1 - ) C TagBox["C", FresnelC] ( ( 1 - ) - ( b + ( c - a 2 π 2 ) ) z 2 π ) ( b + c ) ( π a 2 - 2 c + 2 b ) z 2 - ( 1 - ) C TagBox["C", FresnelC] ( ( 1 - ) - ( b + ( π a 2 2 + c ) ) z 2 π ) ( b + c ) - ( 2 b + ( π a 2 + 2 c ) ) z 2 + ( 1 - ) C TagBox["C", FresnelC] ( ( 1 - ) - ( b + 1 2 ( a 2 π - 2 c ) ) z 2 π ) ( b - c ) ( - π a 2 - 2 b + 2 c ) z 2 - ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) ( π a 2 + 2 c + 2 b ) z 2 2 π ) ( b - c ) ( π a 2 + 2 c + 2 b ) z 2 + ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) - ( b + ( c - a 2 π 2 ) ) z 2 π ) ( b + c ) ( π a 2 - 2 c + 2 b ) z 2 + ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) - ( b + ( π a 2 2 + c ) ) z 2 π ) ( b + c ) - ( 2 b + ( π a 2 + 2 c ) ) z 2 - ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) - ( b + 1 2 ( a 2 π - 2 c ) ) z 2 π ) ( b - c ) ( - π a 2 - 2 b + 2 c ) z 2 ) + 8 b z 2 C TagBox["C", FresnelC] ( a z ) ( b sin ( c z 2 ) - c cos ( c z 2 ) ) b 2 + c 2 ) z z b z 2 c z 2 FresnelC a z 1 16 a 2 1 2 z b -1 c -1 a 2 -1 2 b 2 c z 2 1 2 -1 -1 b c a 2 -1 2 c 2 b z 2 1 2 -1 b -1 c a 2 2 c 2 b z 2 1 2 -1 -1 b c -1 2 b a 2 2 c z 2 1 2 -1 1 -1 FresnelC 1 -1 a 2 2 c 2 b z 2 1 2 2 1 2 -1 b -1 c a 2 2 c 2 b z 2 1 2 -1 -1 1 -1 FresnelC 1 -1 -1 b c -1 a 2 2 -1 z 2 1 2 1 2 -1 b c a 2 -1 2 c 2 b z 2 1 2 -1 -1 1 -1 FresnelC 1 -1 -1 b a 2 2 -1 c z 2 1 2 1 2 -1 b c -1 2 b a 2 2 c z 2 1 2 -1 1 -1 FresnelC 1 -1 -1 b 1 2 a 2 -1 2 c z 2 1 2 1 2 -1 b -1 c -1 a 2 -1 2 b 2 c z 2 1 2 -1 -1 1 FresnelS 1 -1 a 2 2 c 2 b z 2 1 2 2 1 2 -1 b -1 c a 2 2 c 2 b z 2 1 2 -1 1 FresnelS 1 -1 -1 b c -1 a 2 2 -1 z 2 1 2 1 2 -1 b c a 2 -1 2 c 2 b z 2 1 2 -1 1 FresnelS 1 -1 -1 b a 2 2 -1 c z 2 1 2 1 2 -1 b c -1 2 b a 2 2 c z 2 1 2 -1 -1 1 FresnelS 1 -1 -1 b 1 2 a 2 -1 2 c z 2 1 2 1 2 -1 b -1 c -1 a 2 -1 2 b 2 c z 2 1 2 -1 8 b z 2 FresnelC a z b c z 2 -1 c c 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