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 FresnelC

 http://functions.wolfram.com/06.33.21.0095.01

 Input Form

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

 Standard Form

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FractionBox[RowBox[List["8", " ", "\[ImaginaryI]", " ", SuperscriptBox["\[ExponentialE]", RowBox[List["b", " ", SuperscriptBox["z", "2"]]]], " ", RowBox[List["FresnelC", "[", RowBox[List["a", " ", "z"]], "]"]], " ", RowBox[List["(", RowBox[List[RowBox[List[RowBox[List["-", "c"]], " ", RowBox[List["Cosh", "[", RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "]"]]]], "+", RowBox[List["b", " ", RowBox[List["Sinh", "[", RowBox[List["c", " ", SuperscriptBox["z", "2"]]], "]"]]]]]], ")"]]]], RowBox[List[SuperscriptBox["b", "2"], "-", SuperscriptBox["c", "2"]]]]]], ")"]]]]]]]]

 MathML Form

 z b z 2 sinh ( 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 b - 2 c ) z 2 - ( b - c ) ( π a 2 - 2 b + 2 c ) z 2 + ( b + c ) - ( 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 ) ( b - c ) ( - 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 ) ( b + c ) ( 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 ) ( b - c ) ( 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 ) ( b + c ) - ( π a 2 + 2 b + 2 c ) z 2 + ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) ( - π a 2 - 2 b + 2 c ) z 2 2 π ) ( b - c ) ( - π a 2 - 2 b + 2 c ) z 2 - ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) - ( - π a 2 + 2 b + 2 c ) z 2 2 π ) ( b + c ) ( π a 2 - 2 b - 2 c ) z 2 + ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) ( π a 2 - 2 b + 2 c ) z 2 2 π ) ( b - c ) ( π a 2 - 2 b + 2 c ) z 2 - ( 1 + ) S TagBox["S", FresnelS] ( ( 1 - ) - ( π a 2 + 2 b + 2 c ) z 2 2 π ) ( b + c ) - ( π a 2 + 2 b + 2 c ) z 2 ) + 8 b z 2 C TagBox["C", FresnelC] ( a z ) ( b sinh ( c z 2 ) - c cosh ( c z 2 ) ) b 2 - c 2 ) z z b z 2 c z 2 FresnelC a z -1 1 16 a 2 1 2 z -1 b -1 c -1 a 2 -1 2 b 2 c z 2 1 2 -1 b c a 2 -1 2 b -1 2 c z 2 1 2 -1 -1 b -1 c a 2 -1 2 b 2 c z 2 1 2 -1 b c -1 a 2 2 b 2 c z 2 1 2 -1 -1 1 -1 FresnelC 1 -1 -1 a 2 -1 2 b 2 c z 2 1 2 2 1 2 -1 b -1 c -1 a 2 -1 2 b 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 b c a 2 -1 2 b -1 2 c z 2 1 2 -1 -1 1 -1 FresnelC 1 -1 a 2 -1 2 b 2 c z 2 1 2 2 1 2 -1 b -1 c a 2 -1 2 b 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 b c -1 a 2 2 b 2 c z 2 1 2 -1 1 FresnelS 1 -1 -1 a 2 -1 2 b 2 c z 2 1 2 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 -1 -1 a 2 2 b 2 c z 2 1 2 2 1 2 -1 b c a 2 -1 2 b -1 2 c z 2 1 2 -1 1 FresnelS 1 -1 a 2 -1 2 b 2 c z 2 1 2 2 1 2 -1 b -1 c a 2 -1 2 b 2 c z 2 1 2 -1 -1 1 FresnelS 1 -1 -1 a 2 2 b 2 c z 2 1 2 2 1 2 -1 b c -1 a 2 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 -1 c 2 -1 [/itex]

 Rule Form

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

 2001-10-29

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