2013/02/28 by Antonio R. Vargas
Mathematics · #Analytic Number Theory Research #Holomorphic and Operator Theory #Meromorphic and Entire Functions #math.CA #math.NT
paper · pdf · doi:10.1007/s00365-014-9241-7
published as Constructive Approximation, 40 (2014), No. 2, pp. 219-239 · 19 pages, 5 figures. arXiv admin note: text overlap with arXiv:1208.5186
arxiv created 2014/05/27 · openalex publication_date 2014/07/11 · arxiv updated 2015/03/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/29
We are interested in studying the asymptotic behavior of the zeros of partial sums of power series for a family of entire functions defined by exponential integrals. The zeros grow on the order of O(n), and after rescaling we explicitly calculate their limit curve. We find that the rate that the zeros approach the curve depends on the order of the singularities/zeros of the integrand in the exponential integrals. As an application of our findings we derive results concerning the zeros of partial sums of power series for Bessel functions of the first kind.