The distribution of zeros of a class of Jacobi polynomials

Abstract

Polynomials whose coefficients are successive derivatives of a class of generalized Laguerre polynomials evaluated at x = 0 x=0 are shown to be stable. These polynomials can be expressed in terms of Jacobi polynomials. The authors also prove that a related family of polynomials, depending on a parameter, possess only real and negative zeros. A special class of stability-preserving operators is also investigated.