Barton Willis <willisb at unk.edu> writes:
> For Dirac delta integration at a jump discontinuity, see, for example,
> http://dlmf.nist.gov/1.17 (Eq. 1.17.7) There are, of course, variants
> that yield a different linear combination of the left and right
> limits.
Well, yes, they give a formula. But this just means that the people who
wrote the DLMF made an arbitrary decision that delta should be
approximated by symmetric functions.
I don't really know why they specify this representation by exponentials
in 1.17.5: they'll get the same result with any sequence of symmetric
Riemann integrable symmetric functions whose supports vanish in the
right way and that have integrals equal to one. For example, you could
take a=1/2 in the example I sent this morning and just get a box
integral. Something with an exp(-x^2) in it just seems perversely hard
to integrate!
But maybe I'm missing something? I don't *think* that it matters that
the functions are smooth, for example.
Rupert
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