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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).

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