  Let $\nu_{\alpha,q}$ be the probability and orthogonality measure for the
$q$-Meixner-Pollaczek orthogonal polynomials, which has appeared in
\cite{BEH15} as the distribution of the $(\alpha,q)$-Gaussian process (the
Gaussian process of type B) over the $(\alpha,q)$-Fock space (the Fock space of
type B). The main purpose of this paper is to find the radial Bargmann
representation of $\nu_{\alpha,q}$. Our main results cover not only the
representation of $q$-Gaussian distribution by \cite{LM95}, but also of
$q^2$-Gaussian and symmetric free Meixner distributions on $\mathbb R$. In
addition, non-trivial commutation relations satisfied by $(\alpha,q)$-operators
are presented.
