On asymptotic constants related to products of Bernoulli numbers and factorials. (English) Zbl 1163.11014

Summary: 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.


11B68 Bernoulli and Euler numbers and polynomials
11B65 Binomial coefficients; factorials; \(q\)-identities
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