NOTE ON THE IRRATIONALITY OF CERTAIN MULTIVARIATE $q$-FUNCTIONS

Abstract

Various irrationality results on certain infinite series and products representing q-functions were established in recent years by Borwein, Lubinsky, and Zhou [1], [7-10]. In all these papers, Pad´e approximants to appropriate functions were constructed to produce rational approximations that are too rapid to be consistent with rationality. The main purpose of this note is to show how an old and seemingly forgotten irrationality criterion of the present author [3], particularly suited for q-functions, can be used to deduce very easily much more general results.