Popa's "Recurrent Sequences" and Reciprocity

TL;DR

This paper investigates the numerical evaluation of constants in asymptotic expansions for nonlinear recurrences, building on Popa's work, using variable transformations and specific algorithms.

Contribution

It introduces a method involving reciprocal transformations and the Mavecha & Laohakosol algorithm to compute constants in Popa's asymptotic expansions.

Findings

Successful numerical evaluation of constants in Popa's recurrences

Enhanced computational techniques for nonlinear recurrence analysis

Validation of asymptotic expansion accuracy

Abstract

Dumitru Popa found asymptotic expansions for certain nonlinear recurrences, but left open the numerical evaluation of associated constants. We address this issue. A change of variables involving reciprocals and the algorithm of Mavecha & Laohakosol play a key role in our computations.