Transcendental Numbers and the Lambert-Tsallis Function
Abstract
To decide upon the arithmetic nature of some numbers may be a non-trivial problem. Some cases are well know, for example exp(1) and W(1), where W is the Lambert function, are transcendental numbers. The Tsallis q-exponential, eq (z), and the Lambert-Tsallis Wq (z) function, where q is a real parameter, are, respectively, generalizations of the exponential and Lambert functions. In the present work we use the Gelfond-Schneider theorem in order to show the arithmetic conditions on q and z such that Wq (z) and expq (z) are transcendental.
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