Little q-Jacobi polynomials

Summary

The little $q$-Jacobi polynomials $p_n(x; a, b \mid q)$ are a family of orthogonal polynomials defined by a terminating basic hypergeometric series. They are orthogonal for a discrete weight carried by the points $q^k$ with $k = 0, 1, 2, \ldots$. As $q \to 1$ with $a = q^\alpha$ and $b = q^\beta$, they tend to the Jacobi polynomials in a shifted variable. They belong to the $q$-analogue of the Askey scheme.