Large-order perturbation theory of linear eigenvalue problems
Classical Analysis and ODEs
2026-02-04 v2 General Relativity and Quantum Cosmology
Quantum Physics
Abstract
We consider a class of linear eigenvalue problems depending on a small parameter epsilon in which the series expansion for the eigenvalue in powers of epsilon is divergent. We develop a new technique to determine the precise nature of this divergence. We illustrate the technique through its application to four examples: the anharmonic oscillator, a simplified model of equatorially-trapped Rossby waves, and two simplified models based on quasinormal modes of Reissner-Nordstrom-de Sitter black holes.
Cite
@article{arxiv.2509.14763,
title = {Large-order perturbation theory of linear eigenvalue problems},
author = {Stephen Jonathan Chapman},
journal= {arXiv preprint arXiv:2509.14763},
year = {2026}
}
Comments
5 figures