Francisco Javier Toledo (Centro de Investigación Operativa, Universidad Miguel Hernández de Elche)
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 the whole set of initial data which ensure their convergence or divergence.