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 FresnelC

 http://functions.wolfram.com/06.33.21.0098.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29

© 1998-2013 Wolfram Research, Inc.