On Non-linear Characterizations of Classical Orthogonal Polynomials

Abstract Classical orthogonal polynomials are known to satisfy seven equivalent properties, namely the Pearson equation for linear functional, second-order differential/difference/ q -differential/ divided-difference equation, orthogonality of derivatives, Rodrigues formula, two types structure relations, and Riccati formal Stieltjes function. In this work, following previous work by Kil et al. (J Differ Equ Appl 4:145–162, 1998a; Kyungpook Math J 38:259–281, 1998b), we state prove a non-linear characterization result classical on non-uniform lattices. Next, give explicit relations some families these classes.