  q-deformed oscillators and the q-Bose gas model enable effective description
of the observed non-Bose type behavior of the intercept ("strength")
$\lambda^{(2)}\equiv C^{(2)}(K,K)-1$ of two-particle correlation function
$C^{(2)}(p_1,p_2)$ of identical pions produced in heavy-ion collisions. Three-
and n-particle correlation functions of pions (or kaons) encode more
information on the nature of the emitting sources in such experiments. And so,
the q-Bose gas model was further developed: the intercepts of n-th order
correlators of q-bosons and the n-particle correlation intercepts within the
q,p-Bose gas model have been obtained, the result useful for quantum optics,
too. Here we present the combined analysis of two- and three-pion correlation
intercepts for the q-Bose gas model and its q,p-extension, and confront with
empirical data (from CERN SPS and STAR/RHIC) on pion correlations. Similar to
explicit dependence of $\lambda^{(2)}$ on mean momenta of particles (pions,
kaons) found earlier, here we explore the peculiar behavior, versus mean
momentum, of the 3-particle correlation intercept $\lambda^{(3)}(K)$. The whole
approach implies complete chaoticity of sources, unlike other joint
descriptions of two- and three-pion correlations using two phenomenological
parameters (e.g., core-halo fraction plus partial coherence of sources).
