q-Eulerian polynomials and polynomials with only real zeros
S. -M. Ma, Yi Wang
Abstract
Let f and F be two polynomials satisfying F(x)=u(x)f(x)+v(x)f'(x). We characterize the relation between the location and multiplicity of the real zeros of f and F, which generalizes and unifies many known results, including the results of Brenti and Brändén about the q-Eulerian polynomials.
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