Separation theorems for the zeros of certain hypergeometric polynomials

摘要

We study interlacing properties of the zeros of two contiguous F12 hypergeometric polynomials. We use the connection between hypergeometric F12 and Jacobi polynomials, as well as a monotonicity property of zeros of orthogonal polynomials due to Markoff, to prove that the zeros of contiguous hypergeometric polynomials separate each other. We also discuss interlacing results for the zeros of F12 and those of the polynomial obtained by shifting one of the parameters of F12 by ±t where 0