Expanding Dirac delta function with Hermite polynomial

Plugging the series into Wolfram Alpha gives us that it diverges, see here. So the expansions seems to be valid. Just a minor thing: it is usually a trap to actually evaluate distributions like the Dirac function, as they are not actually functions and only really make sense under an integral sign. Viewing it as a functional with the property you listed at the top is much more clear and avoids function having infinite values and other weird stuff.

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Dirac Delta

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