On the convergence of infinite towers of powers and logarithms for general initial data: applications to LambertW function sequences

Abstract

The objective of this paper is to provide the exact sets of initial data ensuring the convergence or divergence of a special class of real towers of powers and logarithms. All the terms forming these towers have a common value except the cusp element, that is indeed the initial data of the sequences defining the towers. The results obtained will be applied to some Lambert W function sequences, providing also thewhole set of initial datawhich ensure their convergence or divergence.