Rational approximation of Euler's constant using multiple orthogonal polynomials

Autor:	Wolfs, Thomas, Van Assche, Walter
Rok vydání:	2024
Předmět:	Mathematics - Number Theory Mathematics - Classical Analysis and ODEs 11J13 11J72 33C45 42C05
Druh dokumentu:	Working Paper
Popis:	We construct new rational approximants of Euler's constant that improve those of Aptekarev et al. (2007) and Rivoal (2009). The approximants are given in terms of certain (mixed type) multiple orthogonal polynomials associated with the exponential integral. The dual family of multiple orthogonal polynomials leads to new rational approximants of the Gompertz constant that improve those of Aptekarev et al. (2007). Our approach is motivated by the fact that we can reformulate Rivoal's construction in terms of type I multiple Laguerre polynomials of the first kind by making use of the underlying Riemann-Hilbert problem. As a consequence, we can drastically simplify Rivoal's approach, which allows us to study the Diophantine and asymptotic properties of the approximants more easily. Comment: 23 pages. v2: added some references to other known constructions
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2404.09799 Zobrazit plný text záznamu View this record from Arxiv