I would like to find the speed of divergence of $\prod_{m=1}^n (\frac{z}{m} + 1)^m$ for any $z$. For example, if $|z| < 1$, doing taylor expansion we know that it is roughly $e^{zn}.$ But I need it for all $z$ such that $\mathrm{Re}(z) > -1.$
2026-04-02 04:33:28.1775104408
speed of divergence of $\prod_{m=1}^n (\frac{z}{m} + 1)^m$
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