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/06.28.21.0103.01

 Input Form

 Integrate[z^3 E^(b z) Sinh[c z] Erfi[a z], z] == (1/(16 a^6 Sqrt[Pi])) E^(a^2 z^2) ((1/(b - c)^4) (2 a (b - c) E^((b - c) z) ((b - c)^4 - 2 a^2 (b - c)^2 (-1 + b z - c z) + 4 a^4 (6 - 3 (b - c) z + (b - c)^2 z^2)) - 8 a^6 E^(z (b - c - a^2 z)) Sqrt[Pi] (-6 + 6 (b - c) z - 3 (b - c)^2 z^2 + (b - c)^3 z^3) Erfi[a z] + (-48 a^6 - 12 a^4 (b - c)^2 - (b - c)^6) E^(-((b - c)^2/(4 a^2)) - a^2 z^2) Sqrt[Pi] Erfi[(b - c)/(2 a) + a z]) - (1/(b + c)^4) (2 a (b + c) E^((b + c) z) ((b + c)^4 - 2 a^2 (b + c)^2 (-1 + b z + c z) + 4 a^4 (6 - 3 (b + c) z + (b + c)^2 z^2)) - 8 a^6 E^(z (b + c - a^2 z)) Sqrt[Pi] (-6 + 6 (b + c) z - 3 (b + c)^2 z^2 + (b + c)^3 z^3) Erfi[a z] + (-48 a^6 - 12 a^4 (b + c)^2 - (b + c)^6) E^(-((b + c)^2/(4 a^2)) - a^2 z^2) Sqrt[Pi] Erfi[(b + c)/(2 a) + a z]))

 Standard Form

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 MathML Form

 z 3 b z sinh ( c z ) erfi ( a z ) z 1 16 a 6 π a 2 z 2 ( 1 ( b - c ) 4 ( - 8 z ( - z a 2 + b - c ) π ( ( b - c ) 3 z 3 - 3 ( b - c ) 2 z 2 + 6 ( b - c ) z - 6 ) erfi ( a z ) a 6 + 2 ( b - c ) ( b - c ) z ( 4 ( ( b - c ) 2 z 2 - 3 ( b - c ) z + 6 ) a 4 - 2 ( b - c ) 2 ( b z - c z - 1 ) a 2 + ( b - c ) 4 ) a + ( - 48 a 6 - 12 ( b - c ) 2 a 4 - ( b - c ) 6 ) - ( b - c ) 2 4 a 2 - a 2 z 2 π erfi ( b - c 2 a + a z ) ) - 1 ( b + c ) 4 ( - 8 z ( - z a 2 + b + c ) π ( ( b + c ) 3 z 3 - 3 ( b + c ) 2 z 2 + 6 ( b + c ) z - 6 ) erfi ( a z ) a 6 + 2 ( b + c ) ( b + c ) z ( 4 ( ( b + c ) 2 z 2 - 3 ( b + c ) z + 6 ) a 4 - 2 ( b + c ) 2 ( b z + c z - 1 ) a 2 + ( b + c ) 4 ) a + ( - 48 a 6 - 12 ( b + c ) 2 a 4 - ( b + c ) 6 ) - ( b + c ) 2 4 a 2 - a 2 z 2 π erfi ( b + c 2 a + a z ) ) ) z z 3 b z c z Erfi a z 1 16 a 6 1 2 -1 a 2 z 2 1 b -1 c 4 -1 -8 z -1 z a 2 b -1 c 1 2 b -1 c 3 z 3 -1 3 b -1 c 2 z 2 6 b -1 c z -6 Erfi a z a 6 2 b -1 c b -1 c z 4 b -1 c 2 z 2 -1 3 b -1 c z 6 a 4 -1 2 b -1 c 2 b z -1 c z -1 a 2 b -1 c 4 a -48 a 6 -1 12 b -1 c 2 a 4 -1 b -1 c 6 -1 b -1 c 2 4 a 2 -1 -1 a 2 z 2 1 2 Erfi b -1 c 2 a -1 a z -1 1 b c 4 -1 -8 z -1 z a 2 b c 1 2 b c 3 z 3 -1 3 b c 2 z 2 6 b c z -6 Erfi a z a 6 2 b c b c z 4 b c 2 z 2 -1 3 b c z 6 a 4 -1 2 b c 2 b z c z -1 a 2 b c 4 a -48 a 6 -1 12 b c 2 a 4 -1 b c 6 -1 b c 2 4 a 2 -1 -1 a 2 z 2 1 2 Erfi b c 2 a -1 a z [/itex]

 Rule Form

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

 2001-10-29