Updates:
Labels: -Milestone-Release0.7.0
Comment #13 on issue 841 by asmeurer: integrate(exp(-x**2)*exp(I*k*x), (x,
-oo, oo)) doesn't calculate the integral
http://code.google.com/p/sympy/issues/detail?id=841
Another (and in my opinion, better, until we can get the solution mentioned
in comment 3) way would be to fix the indefinite integral to work. From
Maple:
integrate(exp(-x**2)*exp(I*k*x), x);
1 (1/2) / 1 2\ / 1 \
- - Pi exp|- - k | erf|-x + - I k|
2 \ 4 / \ 2 /
In fact, the general integral of an exponential of a quadratic is an error
function:
integrate(exp(a*x**2 + b*x + c), x);
/ 2 \
(1/2) | b | / (1/2) b \
Pi exp|c - ---| erf|-(-a) x + -----------|
\ 4 a/ | (1/2)|
\ 2 (-a) /
- ----------------------------------------------------
(1/2)
2 (-a)
Once I finish risch_integrate() (issue 2010), I will probably write some
routines to convert nonelementary integrals of this form into error
functions. But feel free to implement this in heurisch or elsewhere before
then.
This solution is *much* better than the one given in that patch, because it
will work for any limits, or no limits, instead of just -oo to oo.
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