Second order determinants for three-term recurrence polynomial sequences
DOI:
https://doi.org/10.2298/FIL2609169MKeywords:
Reverse Tur\'an expression, x-log-concavity, three-term recurrence polynomial, orthogonal polynomialAbstract
In this paper, we present some sufficient conditions for the sign of second order determinants for Hankel matrices of three-term recurrence polynomial sequences. As applications, we confirm two conjectures of Z.-H. Sun on the reverse Tur\'an expression for two polynomial sequences $G_n(x)$ and $V_n(x)$. In addition, we show that all the zeros of $G_n(x)$ and $V_n(x)$ lie on the line $\Re(x)=-1/2$.
