I would like to sum the following $$\sum_{n=1}^{\infty}\frac{1}{n^b(n+m)^b}$$ for values of $b$ for which the sum exists. The problem is that truncating the sum does not work that good, and needs in general large number of terms specially when $b$ is close to non-summability areas. I then tried to rewrite the sum into some function for which we might have convenient and precise ways to calculate them. Unfortunately have not been successful. I appreciate any ideas. Many thanks!
2026-04-03 01:30:22.1775179822
convenient and precise calculation of $\sum_{n=1}^{\infty}\frac{1}{n^b(n+m)^b}$
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