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/06.25.21.0045.01

 Input Form

 Integrate[z^3 Cos[b z] Erf[a z], z] == (E^(-(b^2/(4 a^2)) - I b z - a^2 z^2) (-48 I a^5 b E^(b^2/(4 a^2)) - 4 I a^3 b^3 E^(b^2/(4 a^2)) - 2 I a b^5 E^(b^2/(4 a^2)) + 48 I a^5 b E^((1/4) b (b/a^2 + 8 I z)) + 4 I a^3 b^3 E^((1/4) b (b/a^2 + 8 I z)) + 2 I a b^5 E^((1/4) b (b/a^2 + 8 I z)) + 24 a^5 b^2 E^(b^2/(4 a^2)) z + 4 a^3 b^4 E^(b^2/(4 a^2)) z + 24 a^5 b^2 E^((1/4) b (b/a^2 + 8 I z)) z + 4 a^3 b^4 E^((1/4) b (b/a^2 + 8 I z)) z + 8 I a^5 b^3 E^(b^2/(4 a^2)) z^2 - 8 I a^5 b^3 E^((1/4) b (b/a^2 + 8 I z)) z^2 + (48 a^6 + 12 a^4 b^2 + b^6) E^(z (I b + a^2 z)) Sqrt[Pi] Erf[(I b + 2 a^2 z)/(2 a)] - 48 I a^6 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] - 12 I a^4 b^2 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] - I b^6 E^(z (I b + a^2 z)) Sqrt[Pi] Erfi[b/(2 a) + I a z] + 8 a^6 E^(b^2/(4 a^2) + a^2 z^2) Sqrt[Pi] Erf[a z] (3 (-2 - 2 I b z + b^2 z^2 + E^(2 I b z) (-2 + 2 I b z + b^2 z^2)) + 2 b^3 E^(I b z) z^3 Sin[b z])))/(16 a^6 b^4 Sqrt[Pi])

 Standard Form

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 MathML Form

 z 3 cos ( b z ) erf ( a z ) z 1 16 a 6 b 4 π ( - b 2 4 a 2 - z b - a 2 z 2 ( - 48 z ( z a 2 + b ) π erfi ( b 2 a + a z ) a 6 + 8 b 2 4 a 2 + a 2 z 2 π erf ( a z ) ( 2 b 3 b z sin ( b z ) z 3 + 3 ( b 2 z 2 - 2 b z + 2 b z ( b 2 z 2 + 2 b z - 2 ) - 2 ) ) a 6 - 8 b 3 1 4 b ( b a 2 + 8 z ) z 2 a 5 + 8 b 3 b 2 4 a 2 z 2 a 5 - 48 b b 2 4 a 2 a 5 + 48 b 1 4 b ( b a 2 + 8 z ) a 5 + 24 b 2 b 2 4 a 2 z a 5 + 24 b 2 1 4 b ( b a 2 + 8 z ) z a 5 - 12 b 2 z ( z a 2 + b ) π erfi ( b 2 a + a z ) a 4 - 4 b 3 b 2 4 a 2 a 3 + 4 b 3 1 4 b ( b a 2 + 8 z ) a 3 + 4 b 4 b 2 4 a 2 z a 3 + 4 b 4 1 4 b ( b a 2 + 8 z ) z a 3 - 2 b 5 b 2 4 a 2 a + 2 b 5 1 4 b ( b a 2 + 8 z ) a + ( 48 a 6 + 12 b 2 a 4 + b 6 ) z ( z a 2 + b ) π erf ( 2 z a 2 + b 2 a ) - b 6 z ( z a 2 + b ) π erfi ( b 2 a + a z ) ) ) z z 3 b z Erf a z 1 16 a 6 b 4 1 2 -1 -1 b 2 4 a 2 -1 -1 z b -1 a 2 z 2 -48 z z a 2 b 1 2 Erfi b 2 a -1 a z a 6 8 b 2 4 a 2 -1 a 2 z 2 1 2 Erf a z 2 b 3 b z b z z 3 3 b 2 z 2 -1 2 b z 2 b z b 2 z 2 2 b z -2 -2 a 6 -1 8 b 3 1 4 b b a 2 -1 8 z z 2 a 5 8 b 3 b 2 4 a 2 -1 z 2 a 5 -1 48 b b 2 4 a 2 -1 a 5 48 b 1 4 b b a 2 -1 8 z a 5 24 b 2 b 2 4 a 2 -1 z a 5 24 b 2 1 4 b b a 2 -1 8 z z a 5 -1 12 b 2 z z a 2 b 1 2 Erfi b 2 a -1 a z a 4 -1 4 b 3 b 2 4 a 2 -1 a 3 4 b 3 1 4 b b a 2 -1 8 z a 3 4 b 4 b 2 4 a 2 -1 z a 3 4 b 4 1 4 b b a 2 -1 8 z z a 3 -1 2 b 5 b 2 4 a 2 -1 a 2 b 5 1 4 b b a 2 -1 8 z a 48 a 6 12 b 2 a 4 b 6 z z a 2 b 1 2 Erf 2 z a 2 b 2 a -1 -1 b 6 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