On asymptotic constants related to products of Bernoulli numbers and factorials

Details On asymptotic constants related to products of Bernoulli numbers and factorials On asymptotic constants related to products of Bernoulli numbers and factorials

2006-04-24

arxiv.org/abs/math/0604505v2

Integers 9 (2009), No. 1, Article A08, 83-106

Mathematics

Number Theory

22 pages, final revised version

Scientific paper

10.1515/INTEG.2009.009

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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