3 problems

Ismail's characterization conjecture. Then $(P_n)_{n\geq 0}$ are continuous $q$-Jacobi polynomials, Al-Salam–Chihara polynomials, or special or limiting cases of these families. Mo…

Let $n$ be a positive integer, let $x$ be a variable, and let $a$, $b$, $c$, $d$, and $q$ be parameters. Let $p_n(x;a,b,c,d;q)$ denote the Askey–Wilson polynomial. Quadratic relati…

q-Rodrigues conjecture. The identity