On the number of non-real zeroes of a homogeneous differential polynomial and a generalization of the Laguerre inequalities

Mikhail Tyaglov, Mohamed J. Atia

Given a real polynomial $p$ with only real zeroes, we find upper and lower bounds for the number of non-real zeroes of the differential polynomial $$ F_{\varkappa}[p](z):= p(z)p''(…