From arXiv

We discuss the asymptotic expansions of certain products of Bernoulli numbers and factorials, e.g., \[ \prod_{\nu=1}^n |B_{2\nu}| \quad \text{and} \quad \prod_{\nu=1}^n (k \nu)!^{\nu^r} \quad \text{as} \quad n \to \infty \] for integers $k \geq 1$ and $r \geq 0$. Our main interest is to determine exact expressions, in terms of known constants, for the asymptotic constants of these expansions and to show some relations among them.

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Updated on October 18, 2009

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