LINEAR COMBINATIONS OF POLYNOMIALS WITH THREE-TERM RECURRENCE

We study the zero distribution of the sum of the first n polynomi-als satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a linear combination, whose coefficients are pow-ers of az + b for a, b is an element of R, of Chebyshev polynomials. In particular, we find necessary and sufficient conditions on a, b such that this linear combination is hyperbolic.