## 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.

### MSC:

 11B68 Bernoulli and Euler numbers and polynomials 11B65 Binomial coefficients; factorials; $$q$$-identities
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