Asymptotic evaluation of a function defined by power series

TL;DR

This paper introduces a novel asymptotic evaluation formula for functions defined by power series, applicable to large arguments, using only their power series coefficients, advancing the theory of power series analytic continuation.

Contribution

It provides a new asymptotic evaluation method based solely on power series coefficients, a significant advancement in power series analytic continuation theory.

Findings

Derived a new asymptotic formula for large argument values

Applicable to a defined class of functions

Advances power series analytic continuation theory

Abstract

We present an asymptotic evaluation unitary formula for large argument values existing for defined class of functions. The asymptotic evaluation is obtained using only power series expansion coefficients of a function, what is a new result in power series analytic continuation theory.