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 $H_{m} (z)$ .

PDF Access Denied

We have not been able to recognize your IP address 3.239.119.61 as that of a subscriber to this journal.
Online access to the content of recent issues is by subscription, or purchase of single articles.

Please contact your institution's librarian suggesting a subscription, for example by using our journal-recommendation form. Or, visit our subscription page for instructions on purchasing a subscription.

You may also contact us at contact@msp.org
or by using our contact form.

Or, you may purchase this single article for USD 30.00:

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

PDF Access Denied

Keywords

Mathematical Subject Classification 2010

Milestones

Authors