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; }

 Erfc

 http://functions.wolfram.com/06.27.21.0034.01

 Input Form

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

 Standard Form

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 MathML Form

 z 3 sin ( b z ) erfc ( 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 erfc ( a z ) ( b z ( b 2 z 2 - 3 b z + 2 b z ( b 2 z 2 + 3 b z - 6 ) - 6 ) + 12 b z sin ( b z ) ) a 6 - 48 b b 2 4 a 2 a 5 - 48 b 1 4 b ( b a 2 + 8 z ) a 5 + 8 b 3 b 2 4 a 2 z 2 a 5 + 8 b 3 1 4 b ( b a 2 + 8 z ) z 2 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 Erfc 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 -1 8 b 2 4 a 2 -1 a 2 z 2 1 2 Erfc a z b z b 2 z 2 -1 3 b z 2 b z b 2 z 2 3 b z -6 -6 12 b z b z a 6 -1 48 b b 2 4 a 2 -1 a 5 -1 48 b 1 4 b b a 2 -1 8 z a 5 8 b 3 b 2 4 a 2 -1 z 2 a 5 8 b 3 1 4 b b a 2 -1 8 z z 2 a 5 -1 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 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 -1 4 b 3 1 4 b b a 2 -1 8 z a 3 -1 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 -1 2 b 5 1 4 b b a 2 -1 8 z a -1 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 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