K. Driver

activity

20082020

most citedZeros of the hypergeometric polynomial F(-n,b;c;z)

34 citations · 58 across the 8 of their papers we have counts for

collaborators

10 papers

math.CA2020

Interlacing of zeros of Laguerre polynomials of equal and consecutive degree

J. Arvesú, K. Driver, L. Littlejohn

We investigate interlacing properties of zeros of Laguerre polynomials $L_{n}^{(α)} (x)$ and $L_{n + 1}^{(α + k)} (x),$ $α > - 1,$ where $n \in N$ and $k \in {1, 2}$ . W…

math.CA2020★ 6 cited

Zeros of Jacobi and Ultraspherical polynomials

J. Arvesú, K. Driver, L. Littlejohn

Suppose ${P_{n}^{(α, β)} (x)}_{n = 0}^{\infty}$ is a sequence of Jacobi polynomials with $α, β > - 1.$ We discuss special cases of a question raised by Alan Sokal at OPSFA in 2019, nam…

math.CA2019

Orthogonal sequences constructed from quasi-orthogonal ultraspherical polynomials

Oksana Bihun, Kathy Driver

Let ${x_{k, n - 1}}_{k = 1}^{n - 1}$ and ${x_{k, n}}_{k = 1}^{n},$ $n \in N$ , be two sets of real, distinct points satisfying the interlacing prope…

math.CA2016

Bounds for Extreme Zeros of Quasi-orthogonal Ultraspherical Polynomials

Kathy Driver, Martin E. Muldoon

We discuss and compare upper and lower bounds obtained by two different methods for the positive zero of the ultraspherical polynomial $C_{n}^{(λ)}$ that is greater than $1$ when $…

math.CA2015★ 13 cited

Zeros of Quasi-Orthogonal Jacobi Polynomials

Kathy Driver, Kerstin Jordaan

We consider interlacing properties satisfied by the zeros of Jacobi polynomials in quasi-orthogonal sequences characterised by $α > - 1$ , $- 2 < β < - 1$ . We give necessary and sufficient c…

math.CA2011

Asymptotic zero distribution of a class of hypergeometric polynomials

K. A. Driver, S. J. Johnston

We prove that the zeros of $_{2} F_{1} (- n, \frac{n + 1}{2}; \frac{n + 3}{2}; z)$ asymptotically approach the section of the lemniscate ${z : ∣ z (1 - z)^{2} ∣ = 4/27; Re (z) > 1/3}$ as $n\righ…