Open AccessLinear combinations of polynomials with three-term recurrence
Author(s) -
Khang Tran,
Maverick Zhang
Publication year - 2021
Publication title -
publications de l'institut mathématique
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.246
H-Index - 17
eISSN - 1820-7405
pISSN - 0350-1302
DOI - 10.2298/pim2124029t
Subject(s) - chebyshev polynomials , mathematics , discrete orthogonal polynomials , classical orthogonal polynomials , term (time) , orthogonal polynomials , gegenbauer polynomials , jacobi polynomials , recurrence relation , difference polynomials , zero (linguistics) , pure mathematics , chebyshev equation , combinatorics , mathematical analysis , physics , linguistics , philosophy , quantum mechanics
We study the zero distribution of the sum of the first n polynomials satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a linear combination, whose coefficients are powers of az + b for a, b ? R, of Chebyshev polynomials. In particular, we find necessary and sufficient conditions on a, b such that this linear combination is hyperbolic.