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 FresnelC

 http://functions.wolfram.com/06.33.21.0102.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29