Hi,
I am new to Sage and am trying to reproduce a well known result that
the Fourier Transform of an exponential decay function is a Lorentzian
function.
In other words, the integral of
exp(-abs(k)) * exp(-i2pi*k*x)
with respect to k, from 0 to +infinity (i'm integrating 0 to +inf
instead of -inf to +inf using symmetry),
should yield a Lorentzian function as the result
1/(1+x^2)
However, when I enter into my Sage notebook:
k,x = var('k,x')
f(k,x)=exp(-abs(k))*exp(-I*2*pi*k*x)
integrate(f,k,0,Infinity)
I get back this error:
Traceback (click to the left for traceback)
...
Computation failed due to a bug in Maxima -- NOTE: Maxima had to be
restarted.
If someone can help me understand what I might be doing incorrectly,
that would be greatly appreciated!
Thanks!
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