Transcendental Numbers and the Lambert-Tsallis Function
Number Theory
2020-04-16 v1
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, e_q (z), and the Lambert-Tsallis W_q (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 W_q (z) and exp_q (z) are transcendental.
Cite
@article{arxiv.2004.07101,
title = {Transcendental Numbers and the Lambert-Tsallis Function},
author = {J. L. E. da Silva and R. V. Ramos},
journal= {arXiv preprint arXiv:2004.07101},
year = {2020}
}