sage integration differes from Mathematica
Hi, I'm trying to integrate
E(x) = ae^(-0.5(x/s)^2)cos(fx+phi)
Mathematica
A = Integrate[a Exp[-0.5 x^2/[Sigma]^2] Cos[f x + [Phi]], x]
gives me
0.626657 a E^(-0.5 f^2 [Sigma]^2) [Sigma] (Erf[(0.707107 x)/[Sigma]+(0.+0.707107 I) f [Sigma]] (Cos[[Phi]]-(0.+1. I) Sin[[Phi]])+Erfi[((0.+0.707107 I) x)/[Sigma]+0.707107 f [Sigma]] ((0.-1. I) Cos[[Phi]]+Sin[[Phi]]))
Doing
E = ae^(-0.5(x/s)^2)cos(fx+phi)
A = integrate(E, x)
Sages result is a different one (sorry, cannot copy output, but you can easily reproduce it yourself). The difference isn't obvious at first glance (at least not to me), but you can see it doing e.g.
A /. {a -> 100, f -> 1, [Sigma] -> 8, [Phi] -> 0, x -> 0}
gives 3.11179*10^-15 + 0. I
and Sage
show(A(a=100, f=1, s=8, phi=0, x=0).n())
results in 1.26977421759869e10-11+101.642197289814i
The result differs at least at zero. Anyone any idea what I'm doing wrong?
Cheers!
Ben
