Zeros of polynomials with four-term recurrence

with the initial conditions $H_{0} (z) = 1$ and $H_{- 1} (z) = H_{- 2} (z) = 0$ . We find necessary and sufficient conditions on $b$ and $c$ under which the zeros of $H_{m} (z)$ are real for all $m$ , and provide an explicit real interval on which $⋃_{m = 0}^{\infty} Z (H_{m})$ is dense, where $Z (H_{m})$ is the set of zeros of $H_{m} (z)$ .

Keywords

generating functions, hyperbolic polynomials, recursive sequence

Mathematical Subject Classification 2010

Primary: 30C15, 26C10, 11C08

Milestones

Received: 14 March 2017

Revised: 7 June 2017

Accepted: 19 June 2017

Published: 20 October 2017

Communicated by Kenneth S. Berenhaut

Authors

Khang Tran
Department of Mathematics California State University Fresno, CA United States

Andres Zumba
Department of Mathematics California State University Fresno, CA United States

Vol. 11, No. 3, 2018

Khang Tran and Andres Zumba

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors