Tian-Xiao He

Riordan array representation of recursive polynomial sequences, orthogonal polynomial sequences, and $d$-orthogonal polynomial sequences

We study when a polynomial sequence $\{p_n(x)\}$ satisfying a linear homogeneous recurrence with polynomial coefficients admits an ordinary Riordan array as its coefficient matrix. For second-order recurrences $p_{n+2}(x)=a(x)p_{n+1}(x)+b(x)p_n(x)$, we give a complete characterization. We extend this to a necessary con...