Inversion of perturbation series

TL;DR

This paper explores the inversion and resummation of perturbation series, linking it to parametric perturbation theory, and demonstrates that series reversion can sometimes enhance accuracy through illustrative examples.

Contribution

It introduces a novel connection between perturbation series inversion and parametric perturbation theory, showing potential for improved approximation accuracy.

Findings

Series reversion can improve result accuracy in some cases

Inversion of perturbation series is related to parametric perturbation theory

Illustrative examples demonstrate potential benefits

Abstract

We investigate the inversion of perturbation series and its resummation, and prove that it is related to a recently developed parametric perturbation theory. Results for some illustrative examples show that in some cases series reversion may improve the accuracy of the results.