q-Taylor series, interpolation, and Rodrigues formulas

I will review q-Taylor series for entire functions f(z), and related interpolation questions. For example, can sequences of complex numbers be given such that values of f(z_k) determine f(z), or does f(z_k) being integral imply something about f(z)? For special choices of the points z_k, q-series theorems are the result. Moreover from this viewpoint, a wide class of very well poised basic hypergeometric series always have Rodrigues formulas, including the Askey-Wilson polynomials, ₁₀\phi₉'s, ₁₂\phi₁₁'s and higher. This is joint work with Mourad Ismail.