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/06.25.21.0034.01

 Input Form

 Integrate[z^2 Sin[b z] Erf[a z], z] == (1/(8 a^4 b^3 Sqrt[Pi])) (E^(-(b^2/(4 a^2)) - I b z - a^2 z^2) (8 I a^3 b E^(b^2/(4 a^2)) + 2 I a b^3 E^(b^2/(4 a^2)) - 8 I a^3 b E^((1/4) b (b/a^2 + 8 I z)) - 2 I a b^3 E^((1/4) b (b/a^2 + 8 I z)) - 4 a^3 b^2 E^(b^2/(4 a^2)) z - 4 a^3 b^2 E^((1/4) b (b/a^2 + 8 I z)) z - 4 a^4 E^(b^2/(4 a^2) + a^2 z^2) Sqrt[Pi] (2 I b (-1 + E^(2 I b z)) z + (1 + E^(2 I b z)) (-2 + b^2 z^2)) Erf[a z] - (8 a^4 + 2 a^2 b^2 + b^4) E^(z (I b + a^2 z)) Sqrt[Pi] Erf[(I b + 2 a^2 z)/(2 a)] + 8 I a^4 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] + 2 I a^2 b^2 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] + I b^4 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 2 sin ( b z ) erf ( a z ) z 1 8 a 4 b 3 π ( - b 2 4 a 2 - z b - a 2 z 2 ( - 4 b 2 4 a 2 + a 2 z 2 π ( 2 b ( - 1 + 2 b z ) z + ( 1 + 2 b z ) ( b 2 z 2 - 2 ) ) erf ( a z ) a 4 + 8 z ( z a 2 + b ) π erfi ( b 2 a + a z ) a 4 - 8 b 1 4 b ( b a 2 + 8 z ) a 3 + 8 b b 2 4 a 2 a 3 - 4 b 2 b 2 4 a 2 z a 3 - 4 b 2 1 4 b ( b a 2 + 8 z ) z a 3 + 2 b 2 z ( z a 2 + b ) π erfi ( b 2 a + a z ) a 2 - 2 b 3 1 4 b ( b a 2 + 8 z ) a + 2 b 3 b 2 4 a 2 a - ( 8 a 4 + 2 b 2 a 2 + b 4 ) z ( z a 2 + b ) π erf ( 2 z a 2 + b 2 a ) + b 4 z ( z a 2 + b ) π erfi ( b 2 a + a z ) ) ) z z 2 b z Erf a z 1 8 a 4 b 3 1 2 -1 -1 b 2 4 a 2 -1 -1 z b -1 a 2 z 2 -4 b 2 4 a 2 -1 a 2 z 2 1 2 2 b -1 2 b z z 1 2 b z b 2 z 2 -2 Erf a z a 4 8 z z a 2 b 1 2 Erfi b 2 a -1 a z a 4 -1 8 b 1 4 b b a 2 -1 8 z a 3 8 b b 2 4 a 2 -1 a 3 -1 4 b 2 b 2 4 a 2 -1 z a 3 -1 4 b 2 1 4 b b a 2 -1 8 z z a 3 2 b 2 z z a 2 b 1 2 Erfi b 2 a -1 a z a 2 -1 2 b 3 1 4 b b a 2 -1 8 z a 2 b 3 b 2 4 a 2 -1 a -1 8 a 4 2 b 2 a 2 b 4 z z a 2 b 1 2 Erf 2 z a 2 b 2 a -1 b 4 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