Relations between integrals and series like the one below:

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I know: $$\int_0^1 x^{-x} dx = \sum_1^\infty k^{-k}.$$

I think this is startling and neat at the same time that it has a superficial 'obviousness.' (Though the proof is interesting.) I'm just looking for a search term that would get me to sources discussing these types of relations, and it's hard to ask questions in person during the lockdown. Thanks.