Zeros distribution of the reverse strong Turán expressions of polynomials sequences

Abstract

In this paper, we first show the zeros distribution of the reverse strong Turán expressions of three recurrence polynomials sequences. Then as applications, we obtain the weak (Hurwitz) stability of the reverse strong Turán expressions of Bell polynomials, Dowling polynomials, ordered Bell polynomials, ordered Dowling polynomials and associated Lah polynomials respectively. On the other hand, the reverse strong Turán expressions of Delannoy polynomials, Morgan-Voyce polynomials, many independence polynomials and sextet polynomials have only real zeros respectively. Finally, we present some conjectures related to the Eulerian polynomials and the Narayana polynomials.