  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.
