Weak Hurwitz stability of extended Turán expressions for Stirling--Whitney--Riordan and Laguerre polynomials

Source abstract

In this paper, we establish a sufficient condition for weak Hurwitz stability of extended Turán expressions for the Stirling--Whitney--Riordan polynomials. The proof uses polynomial transformations that preserve zeros in a real interval and in the unit disk. As an application, we prove that the extended Turán expressions for the Bell polynomials are weakly Hurwitz stable. We also prove the corresponding result for the reflected Laguerre polynomials using polynomial approximations. These results settle two conjectures of Chasse, Grabarek, and Visontai.