A new property of a class of Jacobi polynomials

Abstract

Polynomials whose coefficients are successive derivatives of a class of Jacobi polynomials evaluated at x = 1 x=1 are stable. This yields a novel and short proof of the known result that the Bessel polynomials are stable polynomials. Stability-preserving linear operators are discussed. The paper concludes with three open problems involving the distribution of zeros of polynomials.