## On a Rather Surprising Result

Hmm... I have figured out something rather surprising. It is this:

**Claim.** The infinite sum

On the other hand the infinite sum

Thus, both infinite sums are convergent.

One way to prove this is by using hyperbolic sine and hyperbolic cosine Maclaurin expansions. But I argued it differently using (function) eigenvalues.

The proof is detailed in version 11 of "Compendium...", but since there are some ideas that are grossly incomplete (not this proof, I feel it's pretty solid) I haven't gotten around to posting it.

I'm not sure how it fits into the rather big scheme of things yet... but I'm getting there.

Categories: Arithmetic, Functional Analysis, Infinite Sums, Mathematics