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 Erf

 http://functions.wolfram.com/06.25.21.0057.01

 Input Form

 Integrate[z E^(b z) Sin[c z] Erf[a z], z] == ((I/(4 a^2 Sqrt[Pi])) ((1/(b - I c)^2) (2 a (b - I c) E^((b - I c) z) + 2 a^2 E^(z (b - I c + a^2 z)) Sqrt[Pi] (-1 + b z - I c z) Erf[a z] - (2 a^2 - (b - I c)^2) E^((b - I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b - I c)/(2 a) - a z]) - (1/(b + I c)^2) (2 a (b + I c) E^((b + I c) z) + 2 a^2 E^(z (b + I c + a^2 z)) Sqrt[Pi] (-1 + b z + I c z) Erf[a z] - (2 a^2 - (b + I c)^2) E^((b + I c)^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[(b + I c)/(2 a) - a z])))/E^(a^2 z^2)

 Standard Form

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 MathML Form

 z b z sin ( c z ) erf ( a z ) z 4 a 2 π - a 2 z 2 ( 1 ( b - c ) 2 ( 2 z ( z a 2 + b - c ) π ( b z - c z - 1 ) erf ( a z ) a 2 + 2 ( b - c ) ( b - c ) z a - ( 2 a 2 - ( b - c ) 2 ) exp ( ( b - c ) 2 4 a 2 + a 2 z 2 ) π erf ( b - c 2 a - a z ) ) - 1 ( b + c ) 2 ( 2 z ( z a 2 + b + c ) π ( b z + c z - 1 ) erf ( a z ) a 2 + 2 ( b + c ) ( b + c ) z a - ( 2 a 2 - ( b + c ) 2 ) exp ( ( b + c ) 2 4 a 2 + a 2 z 2 ) π erf ( b + c 2 a - a z ) ) ) z z b z c z Erf a z 4 a 2 1 2 -1 -1 a 2 z 2 1 b -1 c 2 -1 2 z z a 2 b -1 c 1 2 b z -1 c z -1 Erf a z a 2 2 b -1 c b -1 c z a -1 2 a 2 -1 b -1 c 2 b -1 c 2 4 a 2 -1 a 2 z 2 1 2 Erf b -1 c 2 a -1 -1 a z -1 1 b c 2 -1 2 z z a 2 b c 1 2 b z c z -1 Erf a z a 2 2 b c b c z a -1 2 a 2 -1 b c 2 b c 2 4 a 2 -1 a 2 z 2 1 2 Erf b c 2 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.