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/06.28.21.0061.01

 Input Form

 Integrate[z E^(b z^2) Sin[c z^2] Erfi[a z], z] == ((-a) b z Sqrt[(-(a^2 + b - I c)) z^2] + I a c z Sqrt[(-(a^2 + b - I c)) z^2] + a b z Sqrt[(-(a^2 + b + I c)) z^2] + I a c z Sqrt[(-(a^2 + b + I c)) z^2] - a (b + I c) z Sqrt[(-(a^2 + b + I c)) z^2] Erf[Sqrt[(-(a^2 + b - I c)) z^2]] + a (b - I c) z Sqrt[(-(a^2 + b - I c)) z^2] Erf[Sqrt[(-(a^2 + b + I c)) z^2]] + 2 I c E^(b z^2) Sqrt[(-(a^2 + b - I c)) z^2] Sqrt[(-(a^2 + b + I c)) z^2] Cos[c z^2] Erfi[a z] - 2 I b E^(b z^2) Sqrt[(-(a^2 + b - I c)) z^2] Sqrt[(-(a^2 + b + I c)) z^2] Erfi[a z] Sin[c z^2])/ (4 (b - I c) ((-I) b + c) Sqrt[(-(a^2 + b - I c)) z^2] Sqrt[(-(a^2 + b + I c)) z^2])

 Standard Form

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 MathML Form

 z b z 2 sin ( c z 2 ) erfi ( a z ) z ( a ( b - c ) - ( a 2 + b - c ) z 2 erf ( - ( a 2 + b + c ) z 2 ) z - a ( b + c ) - ( a 2 + b + c ) z 2 erf ( - ( a 2 + b - c ) z 2 ) z + a b - ( a 2 + b + c ) z 2 z + a c - ( a 2 + b + c ) z 2 z - a b - ( a 2 + b - c ) z 2 z + a c - ( a 2 + b - c ) z 2 z + 2 c b z 2 - ( a 2 + b + c ) z 2 - ( a 2 + b - c ) z 2 cos ( c z 2 ) erfi ( a z ) - 2 b b z 2 - ( a 2 + b - c ) z 2 - ( a 2 + b + c ) z 2 erfi ( a z ) sin ( c z 2 ) ) / ( 4 ( b - c ) ( c - b ) - ( a 2 + b - c ) z 2 - ( a 2 + b + c ) z 2 ) z z b z 2 c z 2 Erfi a z a b -1 c -1 a 2 b -1 c z 2 1 2 Erf -1 a 2 b c z 2 1 2 z -1 a b c -1 a 2 b c z 2 1 2 Erf -1 a 2 b -1 c z 2 1 2 z a b -1 a 2 b c z 2 1 2 z a c -1 a 2 b c z 2 1 2 z -1 a b -1 a 2 b -1 c z 2 1 2 z a c -1 a 2 b -1 c z 2 1 2 z 2 c b z 2 -1 a 2 b c z 2 1 2 -1 a 2 b -1 c z 2 1 2 c z 2 Erfi a z -1 2 b b z 2 -1 a 2 b -1 c z 2 1 2 -1 a 2 b c z 2 1 2 Erfi a z c z 2 4 b -1 c c -1 b -1 a 2 b -1 c z 2 1 2 -1 a 2 b c z 2 1 2 -1 [/itex]

 Rule Form

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

 2001-10-29