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# On asymptotic constants related to products of Bernoulli numbers and factorialsself.__wrap_n=self.__wrap_n||(self.CSS&&CSS.supports("text-wrap","balance")?1:2);self.__wrap_b=(e,t,r)=>{let n=(r=r||document.querySelector([data-br="${e}"])).parentElement,a=e=>r.style.maxWidth=e+"px";r.style.maxWidth="";let s=n.clientWidth,i=n.clientHeight,l=s/2-.25,o=s+.5,u;if(s){for(a(l),l=Math.max(r.scrollWidth,l);l+1<o;)a(u=Math.round((l+o)/2)),n.clientHeight===i?o=u:l=u;a(o*t+s*(1-t))}r.__wrap_o||"undefined"!=typeof ResizeObserver&&(r.__wrap_o=new ResizeObserver(()=>{self.__wrap_b(0,+r.dataset.brr,r)})).observe(n)};self.__wrap_n!=1&&self.__wrap_b(":R12quuultfautta:",1) 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. Simplify Updated on October 18, 2009 Copy BibTeX Edited 2 times Loading... Summary There is no AI-powered summary yet, because we do not have a budget to generate summaries for all articles. 1. Buy subscription We will thank you for helping thousands of people to save their time at the top of the generated summary. If you buy our subscription, you will be able to summarize multiple articles. Pay$8
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