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/06.27.21.0044.01

 Input Form

 Integrate[z^3 Cos[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^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)] - I (-2 a b E^(b^2/(4 a^2)) ((-b^4) (-1 + E^(2 I b z)) + 2 a^2 b^2 (1 + I b z + E^(2 I b z) (-1 + I b z)) + 4 a^4 (6 + 3 I b z - b^2 z^2 + E^(2 I b z) (-6 + 3 I b z + b^2 z^2))) - (48 a^6 + 12 a^4 b^2 + 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] (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])))

 Standard Form

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 MathML Form

 z 3 cos ( b z ) erfc ( a z ) z 1 16 a 6 b 4 π exp ( - b 2 4 a 2 - z b - a 2 z 2 ) ( 8 exp ( b 2 4 a 2 + a 2 z 2 ) π erfc ( 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 - ( 48 a 6 + 12 b 2 a 4 + b 6 ) z ( z a 2 + b ) π erf ( 2 z a 2 + b 2 a ) - ( - 2 a b exp ( b 2 4 a 2 ) ( 4 ( - b 2 z 2 + 3 b z + 2 b z ( b 2 z 2 + 3 b z - 6 ) + 6 ) a 4 + 2 b 2 ( b z + 2 b z ( b z - 1 ) + 1 ) a 2 - b 4 ( - 1 + 2 b z ) ) - ( 48 a 6 + 12 b 2 a 4 + 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 8 b 2 4 a 2 -1 a 2 z 2 1 2 Erfc 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 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 -2 a b b 2 4 a 2 -1 4 -1 b 2 z 2 3 b z 2 b z b 2 z 2 3 b z -6 6 a 4 2 b 2 b z 2 b z b z -1 1 a 2 -1 b 4 -1 2 b z -1 48 a 6 12 b 2 a 4 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