Discriminants of Chebyshev-like polynomials and their generating functions

TL;DR

This paper proves several conjectures by Stolarsky regarding discriminants and generating functions of Chebyshev-like polynomials, employing hypergeometric series techniques and Wilf-Zeilberger pairs.

Contribution

It provides rigorous proofs for Stolarsky's conjectures on Chebyshev-like polynomials' discriminants and generating functions, advancing understanding in this mathematical area.

Findings

Proof of multiple conjectures on discriminants.

Development of methods involving hypergeometric series.

Application of Wilf-Zeilberger pairs in polynomial analysis.

Abstract

In his paper of 2000, Kenneth B. Stolarsky made various observations and conjectures about discriminants and generating functions of certain types of Chebyshev-like polynomials. We prove several of these conjectures. One of our proofs involves Wilf-Zeilberger pairs and a contiguous relation for hypergeometric series.