Self-Similarly Corrected Pade Approximants for the Indeterminate Problem

TL;DR

This paper introduces self-similarly corrected Pade approximants, enhancing their ability to approximate irrational functions and overcoming limitations of standard Pade methods, with demonstrated numerical success in physical examples.

Contribution

The paper presents a novel self-similarly corrected approach that extends Pade approximants to effectively handle irrational functions and divergent sequences.

Findings

Method improves approximation of irrational functions

Numerical examples show convergence where standard Pade fails

Applicable to physical problems with divergent series

Abstract

A method is suggested for treating the well-known deficiency in the use of Pade approximants that are well suited for approximating rational functions, but confront problems in approximating irrational functions. We develop the approach of self-similarly corrected Pade approximants, making it possible to essentially increase the class of functions treated by these approximants. The method works well even in those cases, where the standard Pade approximants are not applicable, resulting in divergent sequences. Numerical convergence of our method is demonstrated by several physical examples.