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The Dirac delta function,
, has the property
In addition, however, the function is singular at
in such a manner
that
![$\displaystyle \int_{-\infty}^\infty \delta (t-t')\,dt' = 1.$](img79.png) |
(18) |
It follows that
![$\displaystyle \int_{-\infty}^\infty f(t)\,\delta(t-t')\,dt' = f(t),$](img80.png) |
(19) |
where
is an arbitrary function that is well behaved at
. It is also easy to see that
![$\displaystyle \delta(t'-t) = \delta(t-t').$](img82.png) |
(20) |
Richard Fitzpatrick
2014-06-27