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/06.28.21.0101.01

 Input Form

 Integrate[z E^(b z) Sinh[c z] Erfi[a z], z] == (I/(4 a^2 Sqrt[Pi])) (E^(a^2 z^2) (-((1/(b - c)^2) (I (2 a (b - c) E^((b - c) z) - (2 a^2 Sqrt[Pi] (-1 + b z - c z) Erfi[a z])/E^(z (-b + c + a^2 z)) - (2 a^2 + (b - c)^2) E^(-((b - c)^2/(4 a^2)) - a^2 z^2) Sqrt[Pi] Erfi[(b - c)/(2 a) + a z]))) + (1/(b + c)^2) (I (2 a (b + c) E^((b + c) z) - 2 a^2 E^(z (b + c - a^2 z)) Sqrt[Pi] (-1 + b z + c z) Erfi[a z] - (2 a^2 + (b + c)^2) 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 b z sinh ( c z ) erfi ( a z ) z 4 a 2 π a 2 z 2 ( 1 ( b + c ) 2 ( ( - 2 z ( - z a 2 + b + c ) π ( b z + c z - 1 ) erfi ( a z ) a 2 + 2 ( b + c ) ( b + c ) z a - ( 2 a 2 + ( b + c ) 2 ) - ( b + c ) 2 4 a 2 - a 2 z 2 π erfi ( b + c 2 a + a z ) ) ) - 1 ( b - c ) 2 ( ( - 2 - z ( z a 2 - b + c ) π ( b z - c z - 1 ) erfi ( a z ) a 2 + 2 ( b - c ) ( b - c ) z a - ( 2 a 2 + ( b - c ) 2 ) - ( b - c ) 2 4 a 2 - a 2 z 2 π erfi ( b - c 2 a + a z ) ) ) ) z z b z c z Erfi a z 4 a 2 1 2 -1 a 2 z 2 1 b c 2 -1 -2 z -1 z a 2 b c 1 2 b z c z -1 Erfi a z a 2 2 b c b c z a -1 2 a 2 b c 2 -1 b c 2 4 a 2 -1 -1 a 2 z 2 1 2 Erfi b c 2 a -1 a z -1 1 b -1 c 2 -1 -2 -1 z z a 2 -1 b c 1 2 b z -1 c z -1 Erfi a z a 2 2 b -1 c b -1 c z a -1 2 a 2 b -1 c 2 -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 [/itex]

 Rule Form

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

 2001-10-29