Limit curves for zeros of sections of exponential integrals
Number Theory
2015-03-17 v4 Classical Analysis and ODEs
Abstract
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.
Keywords
Cite
@article{arxiv.1302.3695,
title = {Limit curves for zeros of sections of exponential integrals},
author = {Antonio R. Vargas},
journal= {arXiv preprint arXiv:1302.3695},
year = {2015}
}
Comments
19 pages, 5 figures. arXiv admin note: text overlap with arXiv:1208.5186