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Have any proposals been advanced for the analytic continuation of the divisor function?

While I was working on the evaluation of a certain series, the following limit came up: \begin{align} \lim_{n \to 1} \frac{d(n)-1}{n(n-1)} &= \lim_{n \to 1} \frac{d'(n)}{2n-1} \\ &= d'(1) .\...
Max Lonysa Muller's user avatar