From Taylor series of analytic functions to their global analysis
Classical Analysis and ODEs
2014-07-28 v1
Abstract
We analyze the conditions on the Taylor coefficients of an analytic function to admit global analytic continuation, complementing a recent paper of Breuer and Simon on general conditions for natural boundaries to form. A new summation method is introduced to convert a relatively wide family of infinite sums and local expansions into integrals. The integral representations yield global information such as analytic continuability, position of singularities, asymptotics for large values of the variable and asymptotic location of zeros.
Keywords
Cite
@article{arxiv.1407.6988,
title = {From Taylor series of analytic functions to their global analysis},
author = {Ovidiu Costin and Xiaoyue Xia},
journal= {arXiv preprint arXiv:1407.6988},
year = {2014}
}