PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 137, Number 10, October 2009, Pages 3259β3269 S 0002-9939(09)09899-2 Article electronically published on March 24, 2009
DISCRIMINANTS OF CHEBYSHEV-LIKE POLYNOMIALS AND THEIR GENERATING FUNCTIONS KHANG TRAN (Communicated by Ken Ono) 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.
1. Introduction We begin by recalling the notion of a discriminant. Suppose that ππ (π₯) is a polynomial of degree π whose roots are π₯1 , π₯2 , . . ., π₯π . Then the disciminant of ππ (π₯), which we will denote by Ξπ₯ ππ (π₯), is β 2πβ2 Ξπ₯ ππ (π₯) = ππ (π₯π β π₯π )2 , 1β€π
