  Motivated by derivation of the Dirac type delta-function for quantum states
in Fock-Bargmann representation, we find q-binomial expansion in terms of
q-Hermite polynomials, analytic in two complex arguments. Based on this
representation, we introduce a new class of complex functions of two complex
arguments, which we call the double q-analytic functions. The real version of
these functions describe the q-analogue of traveling waves, which is not
preserving the shape during evolution as the usual traveling wave. For
corresponding q-wave equation we solve IVP in the q-D'Alembert form.
