Kellner, Bernd C. On asymptotic constants related to products of Bernoulli numbers and factorials. (English) Zbl 1163.11014 Integers 9, No. 1, Article A08, 83-106 (2009). 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. Cited in 1 Document MSC: 11B68 Bernoulli and Euler numbers and polynomials 11B65 Binomial coefficients; factorials; \(q\)-identities PDF BibTeX XML Cite \textit{B. C. Kellner}, Integers 9, No. 1, Article A08, 83--106 (2009; Zbl 1163.11014) Full Text: DOI arXiv EuDML Link OpenURL Online Encyclopedia of Integer Sequences: Decimal expansion of zeta(2)*zeta(3)*zeta(4)*... Decimal expansion of the infinite product of zeta functions for even arguments. Decimal expansion of the infinite product of zeta functions for odd arguments >= 3. Decimal expansion of Product_{n>=1} n! /(sqrt(2*Pi*n) * (n/e)^n * (1+1/n)^(1/12)).