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 Erf

 http://functions.wolfram.com/06.25.21.0033.01

 Input Form

 Integrate[z Sin[b z] Erf[a z], z] == (1/(4 a^2 b^2 Sqrt[Pi])) (E^(-(b^2/(4 a^2)) - I b z - a^2 z^2) (-2 a b E^(b^2/(4 a^2)) - 2 a b E^((1/4) b (b/a^2 + 8 I z)) - 2 a^2 E^(b^2/(4 a^2) + a^2 z^2) Sqrt[Pi] (-I + b z + E^(2 I b z) (I + b z)) Erf[a z] - I (2 a^2 + b^2) E^(z (I b + a^2 z)) Sqrt[Pi] Erf[(I b + 2 a^2 z)/(2 a)] + 2 a^2 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] + b^2 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z]))

 Standard Form

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 MathML Form

 z sin ( b z ) erf ( a z ) z 1 4 a 2 b 2 π exp ( - b 2 4 a 2 - z b - a 2 z 2 ) ( - 2 exp ( b 2 4 a 2 + a 2 z 2 ) π ( - + b z + 2 b z ( + b z ) ) erf ( a z ) a 2 + 2 z ( z a 2 + b ) π erfi ( b 2 a + a z ) a 2 - 2 b b 2 4 a 2 a - 2 b 1 4 b ( b a 2 + 8 z ) a - ( 2 a 2 + b 2 ) z ( z a 2 + b ) π erf ( 2 z a 2 + b 2 a ) + b 2 z ( z a 2 + b ) π erfi ( b 2 a + a z ) ) z z b z Erf a z 1 4 a 2 b 2 1 2 -1 -1 b 2 4 a 2 -1 -1 z b -1 a 2 z 2 -2 b 2 4 a 2 -1 a 2 z 2 1 2 -1 b z 2 b z b z Erf a z a 2 2 z z a 2 b 1 2 Erfi b 2 a -1 a z a 2 -1 2 b b 2 4 a 2 -1 a -1 2 b 1 4 b b a 2 -1 8 z a -1 2 a 2 b 2 z z a 2 b 1 2 Erf 2 z a 2 b 2 a -1 b 2 z z a 2 b 1 2 Erfi b 2 a -1 a z [/itex]

 Rule Form

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

 2001-10-29

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