Large-order perturbation theory of linear eigenvalue problems

Abstract We consider a class of linear eigenvalue problems depending on a small parameter ϵ in which the series expansion for the eigenvalue in powers of ϵ 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–Nordström–de Sitter black holes.