  In the first part of the paper we give a definition of G_q-function and we
establish a regularity result, obtained as a combination of a q-analogue of the
Andre'-Chudnovsky Theorem [And89, VI] and Katz Theorem [Kat70, \S 13].
  In the second part of the paper, we combine it with some formal q-analogous
Fourier transformations, obtaining a statement on the irrationality of special
values of the formal $q$-Borel transformation of a G_q-function.
