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 high order of approximation to illustrate the behavior of the Wilcox expansion.

翻译：我们提出一个框架，其中微分方程解的Fer展开与Wilcox展开源自于为乘积展开播种的初始变换的两个特定选择。在此框架下，中间展开形式也可被设想。我们推导了递推公式。同时给出了Wilcox展开收敛性的一个新下界，以及这些结果的一些应用。特别地，通过两个高阶近似实例演示了Wilcox展开的行为。