Is anyone aware of literature on real-valued functions $f(n)$ for which $\sum_{n=-\infty}^\infty f(n) = \int_{\mathbf{R}}f(x)dx$?

@DescartesBeforetheHorse I do not know whether such functions have been studied in literature, but I have at least try to search with SearchOnMath and Approach0 to see whether I find some posts about this in that way.

I found these post on Mathematics: Finding $f$ such that $ \int f = \sum f$ and A function whose (doubly) infinite sum equals its integral. However, the answers posted there do not say much.

@YCor Now that SEDE is back online, you can use it to search for posts containing the string \color{. Naturally there are more such posts on Mathematics - after all, the site is much bigger.

The above queries return 206 posts on MO and 30591 posts on Math.

No questions with color in the title on MO, 33 such questions on Mathematics.

This question is now posted on Mathematics: If numbered marbles are drawn at random, what is the probability that they sum to $3$?. So I suppose that the MathOverflow copy can be safely deleted.

I see that above - in the searches for titles - I put by mistakes both links to the queries for Mathematics. Here is link for MathOverflow - as I've mentioned, on MathOverflow I did not find posts with color in the title.