## View abstract

### 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. document.getElementById('cloakd3e6a18da027794f8250d45967cafd75').innerHTML = ''; var prefix = '&#109;a' + 'i&#108;' + '&#116;o'; var path = 'hr' + 'ef' + '='; var addyd3e6a18da027794f8250d45967cafd75 = 'j&#111;rd&#97;k' + '&#64;'; addyd3e6a18da027794f8250d45967cafd75 = addyd3e6a18da027794f8250d45967cafd75 + '&#117;n&#105;s&#97;' + '&#46;' + '&#97;c' + '&#46;' + 'z&#97;'; var addy_textd3e6a18da027794f8250d45967cafd75 = 'j&#111;rd&#97;k' + '&#64;' + '&#117;n&#105;s&#97;' + '&#46;' + '&#97;c' + '&#46;' + 'z&#97;';document.getElementById('cloakd3e6a18da027794f8250d45967cafd75').innerHTML += '<a ' + path + '\'' + prefix + ':' + addyd3e6a18da027794f8250d45967cafd75 + '\'>'+addy_textd3e6a18da027794f8250d45967cafd75+'<\/a>';

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).