Session III.7 - Special Functions and Orthogonal Polynomials
Monday, June 19, 14:30 ~ 15:00
Zeros of Meixner polynomials for nonstandard parameter values
Kerstin Jordaan
University of South Africa, South Africa - This email address is being protected from spambots. You need JavaScript enabled to view it.
In this talk I will prove a conjecture in [1] on a lower bound for the first positive zero of a Meixner polynomial when $-\beta,c\in(0,1)$ and use this to identify upper and lower bounds for the first few zeros of Meixner polynomials when $-2 \lt \beta \lt -1$ and $0 \lt c \lt 1$. I will also discuss other properties of the zeros of Meixner polynomials for these parameter ranges.
[1] K. Driver and A. Jooste, Quasi-orthogonal Meixner polynomials, Quaest. Math. 40 (4) (2017), 477-490
Joint work with Alta Jooste (University of Pretoria).