A Unifying Framework for Perturbative Exponential Factorizations

We propose a framework where Fer and Wilcox expansions for the solution of differential equations are derived from two particular choices for the initial transformation that seeds the product expansion. In this scheme, intermediate expansions can also be envisaged. Recurrence formulas are developed. A new lower bound for the convergence of the Wilcox expansion is provided, as well as some applications of the results. In particular, two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.

Automated summary

This paper introduces a framework for deriving Fer and Wilcox expansions for the solution of differential equations from specific choices for the initial transformation of the product expansion. It develops recurrence formulas and provides a new lower bound for the convergence of the Wilcox expansion, along with applications of the results. Two examples are worked out up to a high order of approximation to illustrate the behavior of the Wilcox expansion.