  We expand the Chebyshev polynomials and some of its linear combination in
linear combinations of the q-Hermite, the Rogers (q-utraspherical) and the
Al-Salam--Chihara polynomials and vice versa. We use these expansions to obtain
expansions of some densities, including q-Normal and some related to it, in
infinite series constructed of the products of the other density times
polynomials orthogonal to it, allowing deeper analysis and discovering new
properties. On the way we find an easy proof of expansion of the
Poisson--Mehler kernel as well as its reciprocal. We also formulate simple rule
relating one set of orthogonal polynomials to the other given the properties of
the ratio of the respective densities of measures orthogonalizing these
polynomials sets.
