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; }

 Erf

 http://functions.wolfram.com/06.25.21.0043.01

 Input Form

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

 Standard Form

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 MathML Form

 z cos ( 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 b 2 4 a 2 + a 2 z 2 π erf ( a z ) ( 2 b b z z sin ( b z ) + 2 b z + 1 ) a 2 + ( - 2 a b b 2 4 a 2 ( - 1 + 2 b z ) + ( 2 a 2 + b 2 ) z ( z a 2 + b ) π erf ( 2 z a 2 + b 2 a ) + ( 2 a 2 + 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 Erf a z 2 b b z z b z 2 b z 1 a 2 -2 a b b 2 4 a 2 -1 -1 2 b z 2 a 2 b 2 z z a 2 b 1 2 Erf 2 z a 2 b 2 a -1 2 a 2 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