On the Complex Zeros of Some Families of Orthogonal Polynomials

Abstract EN

The complex zeros of the orthogonal Laguerre polynomials Ln(a)(x) for a<-n, ultraspherical polynomials Pn(λ)(x) for λ<-n, Jacobi polynomials Pn(a,β)(x) for a<-n, β<-n, a+β<-2(n+1), orthonormal Al-Salam-Carlitz II polynomials Pn(a)(x;q) for a<0, 0

Several inequalities regarding the real and imaginary properties of these zeros are given, which help locating their position.

Moreover, a few limit relations regarding the asymptotic behavior of these zeros are proved.

The method used is a functional analytic one.

The obtained results complement and improve previously known results.