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; }

 Erfi

 http://functions.wolfram.com/06.28.21.0034.01

 Input Form

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

 Standard Form

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 MathML Form

 z 2 sin ( b z ) erfi ( a z ) z 1 8 a 4 b 3 π ( - b z ( - 8 1 4 b ( b a 2 + 4 z ) π erfi ( 2 z a 2 + b 2 a ) a 4 - 4 π ( b 2 z 2 - 2 b z + 2 b z ( b 2 z 2 + 2 b z - 2 ) - 2 ) erfi ( a z ) a 4 - 8 b a 2 z 2 a 3 + 8 b z ( z a 2 + 2 b ) a 3 + 4 b 2 a 2 z 2 z a 3 + 4 b 2 z ( z a 2 + 2 b ) z a 3 + 2 b 2 1 4 b ( b a 2 + 4 z ) π erfi ( 2 z a 2 + b 2 a ) a 2 - 2 b 3 z ( z a 2 + 2 b ) a + 2 b 3 a 2 z 2 a + ( 8 a 4 - 2 b 2 a 2 + b 4 ) 1 4 b ( b a 2 + 4 z ) π erf ( b 2 a + a z ) - b 4 1 4 b ( b a 2 + 4 z ) π erfi ( 2 z a 2 + b 2 a ) ) ) z z 2 b z Erfi a z 1 8 a 4 b 3 1 2 -1 -1 b z -8 1 4 b b a 2 -1 4 z 1 2 Erfi 2 z a 2 b 2 a -1 a 4 -1 4 1 2 b 2 z 2 -1 2 b z 2 b z b 2 z 2 2 b z -2 -2 Erfi a z a 4 -1 8 b a 2 z 2 a 3 8 b z z a 2 2 b a 3 4 b 2 a 2 z 2 z a 3 4 b 2 z z a 2 2 b z a 3 2 b 2 1 4 b b a 2 -1 4 z 1 2 Erfi 2 z a 2 b 2 a -1 a 2 -1 2 b 3 z z a 2 2 b a 2 b 3 a 2 z 2 a 8 a 4 -1 2 b 2 a 2 b 4 1 4 b b a 2 -1 4 z 1 2 Erf b 2 a -1 a z -1 b 4 1 4 b b a 2 -1 4 z 1 2 Erfi 2 z a 2 b 2 a -1 [/itex]

 Rule Form

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 Date Added to functions.wolfram.com (modification date)

 2001-10-29