On Oct 8, 10:05 am, achrzesz <[email protected]> wrote:
> The exact integral
>
> 1/2*(erf(pi - 1/2*I) + erf(pi + 1/2*I))*sqrt(pi)*e^(-1/4)
>
> contains *real* expression
>
> (erf(pi - 1/2*I) + erf(pi + 1/2*I))
>
> but maxima/sage can't check that it is real
>
> In WolframAlpha one can check that
>
> Im[Erf[Pi-1/2*I]+Erf[Pi+1/2*I]]
>
> iz zero
>
> Andrzej Chrzeszczyk

Fortunately I was wrong:

sage: w=integrate(exp(-x^2)*cos(x),(x,-pi,pi))/pi
sage: w.imag().full_simplify()
0

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