We study interlacing properties of the zeros of two contiguous 2F1 hypergeometric polynomials. We use the connection between hypergeometric 2F1 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 2F1 and those of the polynomial obtained by shifting one of the parameters of 2F1 by ± t where 0 < t < 1. © 2005 Elsevier B.V. All rights reserved.
Driver, K., & Jordaan, K. (2007). Separation theorems for the zeros of certain hypergeometric polynomials. Journal of Computational and Applied Mathematics, 199(1), 48–55. https://doi.org/10.1016/j.cam.2005.05.039