Effective Summation and Interpolation of Series by Self-Similar Root Approximants

TL;DR

The paper introduces a straightforward analytical technique using self-similar root approximants for summing series, including divergent ones, demonstrating comparable or superior accuracy to Pade approximants across various problems.

Contribution

It presents a novel, general method for summing series using self-similar approximation theory, applicable to divergent series and outperforming traditional Pade approximants in many cases.

Findings

Effective summation of divergent series achieved

Method's accuracy is comparable or superior to Pade approximants

Applicable to a wide range of problems

Abstract

We describe a simple analytical method for effective summation of series, including divergent series. The method is based on self-similar approximation theory resulting in self-similar root approximants. The method is shown to be general and applicable to different problems, as is illustrated by a number of examples. The accuracy of the method is not worse, and in many cases better, than that of Pade approximants, when the latter can be defined.