# Delta function could not be got when delta function is the answer

Discussion in 'Mathematica' started by PengYu.UT, Feb 11, 2006.

1. ### PengYu.UTGuest

Sum[E^(-2*Pi*I*n*p*k), {n, -Infinity, Infinity}]

The above summation should give an delta function. However, 0 is given
by Mathematica 5.0. Is it a bug. Is there any workaround to get the
delta function?

Thanks,
Peng

PengYu.UT, Feb 11, 2006

2. ### albertGuest

which is no function but a distribution (or generalized function)...
which is correct for almost every p and k
depends on what you expect that mathematica can do. As far as I know, it can
handle the delta function only to some extend in some functions like
Integrate but does not claim to support distributions in general (see
documentation for DiracDelta and 'Generalized Functions'). But maybe I am
wrong here, I personally wouldn't expect mathematica to do too much useful
stuff with DiracDelta especially if it is not in the realm of D, Integrate
and FourierTransform...
from the sum you used as input: I don't know.
if input doesn't matter try these :
D[UnitStep[x], x]
FourierTransform[1/Sqrt[2 Pi], k, x]

hth,

albert

albert, Feb 12, 2006

3. ### Pratik DesaiGuest

Check out the site
http://functions.wolfram.com/GeneralizedFunctions/DiracDelta/
among which is this
DiracDelta[x] == Sum[HoldForm[E^(I*k*x)], {k, -Infinity,
Infinity}]/(2*Pi) /; -2*Pi < x < 2*Pi
I added the holdform because mathematica automatically evaluates the sum
to zero, I tried to use
2.5.2 Manipulating Sets of Transformation Rules of m-book but was not
able to apply the transformation??

Hope this helps

Pratik

Pratik Desai, Feb 13, 2006