On approximation measures of q-exponential function

Abstract

We shall present effective approximation measures for certain infinite products related to [Formula: see text]-exponential function [Formula: see text]. There are two main targets. First we shall prove an explicit irrationality measure result for the values [Formula: see text], where [Formula: see text], and [Formula: see text], [Formula: see text]. Then, if we restrict the approximations of [Formula: see text] to rational numbers of the shape [Formula: see text], where [Formula: see text], we may replace Bundschuh’s irrationality exponent [Formula: see text] by [Formula: see text]