AGAIN ON THE IRRATIONALITY OF A CERTAIN INFINITE PRODUCT
Abstract: For fixed complex q with \q\ > 1 let F q ( x , y ) denote the entire function Π (1 + q~*x + q~ixy) of ( x , y ) G C . Very recently, Zhou and Lubinsky proved two 3=0 irrationality results on Fq(r, jf) for positive rational numbers r,s and positive integers q > 1. By simpler arguments we extended their results by showing that, under appropriate hypotheses, Fq(r, f ) cannot belong to K, if r, s e Κ \ {0} and if q is an integer from K. Here Κ is either the rational or an imaginaxy quadratic number field.