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 Erfi

 http://functions.wolfram.com/06.28.21.0043.01

 Input Form

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

 Standard Form

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 MathML Form

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

 Rule Form

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

 2001-10-29