html, body, form { margin: 0; padding: 0; width: 100%; } #calculate { position: relative; width: 177px; height: 110px; background: transparent url(/images/alphabox/embed_functions_inside.gif) no-repeat scroll 0 0; } #i { position: relative; left: 18px; top: 44px; width: 133px; border: 0 none; outline: 0; font-size: 11px; } #eq { width: 9px; height: 10px; background: transparent; position: absolute; top: 47px; right: 18px; cursor: pointer; }

 FresnelC

 http://functions.wolfram.com/06.33.21.0054.01

 Input Form

 Integrate[z^2 E^(b z) Sin[c z] FresnelC[a z], z] == (-(I/(4 a^4 Pi^2))) ((1/(b + I c)^3) (2 a^4 E^((b + I c) z) Pi^2 (2 + (b + I c) z (-2 + b z + I c z)) FresnelC[a z] + (((b + I c)^4 - I a^2 (b + I c)^2 Pi - 2 a^4 Pi^2) (I FresnelC[(b + I c)/(a Pi) - I a z] - FresnelS[(b + I c)/(a Pi) - I a z]))/E^((I (b + I c)^2)/(2 a^2 Pi)) + E^((I (b + I c)^2)/(2 a^2 Pi)) (-(b + I c)^4 - I a^2 (b + I c)^2 Pi + 2 a^4 Pi^2) (I FresnelC[(b + I c)/(a Pi) + I a z] + FresnelS[(b + I c)/(a Pi) + I a z])) - ((2 a E^((b + I c) z))/(b + I c)^2) ((b + I c)^2 Cos[(1/2) a^2 Pi z^2] + a^2 Pi (-2 + b z + I c z) Sin[(1/2) a^2 Pi z^2]) - (1/(b - I c)^3) (2 a^4 E^((b - I c) z) Pi^2 (2 + 2 I c z + b^2 z^2 - c^2 z^2 + 2 b z (-1 - I c z)) FresnelC[a z] + E^((I (b - I c)^2)/(2 a^2 Pi)) (-(b - I c)^4 - I a^2 (b - I c)^2 Pi + 2 a^4 Pi^2) (I FresnelC[(b - I c)/(a Pi) + I a z] + FresnelS[(b - I c)/(a Pi) + I a z]) + (((b - I c)^4 - I a^2 (b - I c)^2 Pi - 2 a^4 Pi^2) (I FresnelC[(b - I c - I a^2 Pi z)/(a Pi)] - FresnelS[(b - I c - I a^2 Pi z)/(a Pi)]))/ E^((I (b - I c)^2)/(2 a^2 Pi)) - 2 a (b - I c) E^((b - I c) z) ((b - I c)^2 Cos[(1/2) a^2 Pi z^2] + a^2 Pi (-2 + b z - I c z) Sin[(1/2) a^2 Pi z^2])))

 Standard Form

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 MathML Form

 z 2 b z sin ( c z ) C TagBox["C", FresnelC] ( a z ) z - 4 a 4 π 2 ( 1 ( b + c ) 3 ( 2 ( b + c ) z π 2 ( ( b + c ) z ( b z + c z - 2 ) + 2 ) C TagBox["C", FresnelC] ( a z ) a 4 + ( b + c ) 2 2 a 2 π ( 2 π 2 a 4 - ( b + c ) 2 π a 2 - ( b + c ) 4 ) ( C TagBox["C", FresnelC] ( b + c a π + a z ) + S TagBox["S", FresnelS] ( b + c a π + a z ) ) + - ( b + c ) 2 2 a 2 π ( - 2 π 2 a 4 - ( b + c ) 2 π a 2 + ( b + c ) 4 ) ( C TagBox["C", FresnelC] ( b + c a π - a z ) - S TagBox["S", FresnelS] ( b + c a π - a z ) ) ) - 2 a ( b + c ) z ( b + c ) 2 ( π ( b z + c z - 2 ) sin ( 1 2 a 2 π z 2 ) a 2 + ( b + c ) 2 cos ( 1 2 a 2 π z 2 ) ) - 1 ( b - c ) 3 ( 2 ( b - c ) z π 2 ( b 2 z 2 - c 2 z 2 + 2 c z + 2 b ( - c z - 1 ) z + 2 ) C TagBox["C", FresnelC] ( a z ) a 4 - 2 ( b - c ) ( b - c ) z ( π ( b z - c z - 2 ) sin ( 1 2 a 2 π z 2 ) a 2 + ( b - c ) 2 cos ( 1 2 a 2 π z 2 ) ) a + - ( b - c ) 2 2 a 2 π ( - 2 π 2 a 4 - ( b - c ) 2 π a 2 + ( b - c ) 4 ) ( 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 2 a 2 π ( 2 π 2 a 4 - ( b - c ) 2 π a 2 - ( b - c ) 4 ) ( C TagBox["C", FresnelC] ( b - c a π + a z ) + S TagBox["S", FresnelS] ( b - c a π + a z ) ) ) ) z z 2 b z c z FresnelC a z -1 4 a 4 2 -1 1 b c 3 -1 2 b c z 2 b c z b z c z -2 2 FresnelC a z a 4 b c 2 2 a 2 -1 2 2 a 4 -1 b c 2 a 2 -1 b c 4 FresnelC b c a -1 a z FresnelS b c a -1 a z -1 b c 2 2 a 2 -1 -2 2 a 4 -1 b c 2 a 2 b c 4 FresnelC b c a -1 -1 a z -1 FresnelS b c a -1 -1 a z -1 2 a b c z b c 2 -1 b z c z -2 1 2 a 2 z 2 a 2 b c 2 1 2 a 2 z 2 -1 1 b -1 c 3 -1 2 b -1 c z 2 b 2 z 2 -1 c 2 z 2 2 c z 2 b -1 c z -1 z 2 FresnelC a z a 4 -1 2 b -1 c b -1 c z b z -1 c z -2 1 2 a 2 z 2 a 2 b -1 c 2 1 2 a 2 z 2 a -1 b -1 c 2 2 a 2 -1 -2 2 a 4 -1 b -1 c 2 a 2 b -1 c 4 FresnelC -1 z a 2 b -1 c a -1 -1 FresnelS -1 z a 2 b -1 c a -1 b -1 c 2 2 a 2 -1 2 2 a 4 -1 b -1 c 2 a 2 -1 b -1 c 4 FresnelC b -1 c a -1 a z FresnelS b -1 c a -1 a z [/itex]

 Rule Form

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

 2001-10-29