Real zeros of 2F1 hypergeometric polynomials

摘要

We use a method based on the division algorithm to determine all the values of the real parameters b and c for which the hypergeometric polynomials 2F1(−n,b;c;z) have n real, simple zeros. Furthermore, we use the quasi-orthogonality of Jacobi polynomials to determine the intervals on the real line where the zeros are located.