Brändén's Conjectures on the Boros-Moll Polynomials
William Y. C. Chen, Donna Q. J. Dou and Arthur L. B. Yang
Abstract: We prove two conjectures of Brändén on the real-rootedness of polynomials Q_{n}(x) and R_{n}(x) which are related to the Boros-Moll polynomials P_{n}(x). In fact, we show that both Q_{n}(x) and R_{n}(x) form Sturm sequences. The first conjecture implies the 2-log-concavity of P_{n}(x), and the second conjecture implies the 3-log-concavity of P_{n}(x). AMS Classification: 26C10; 05A20, 30C15 Keywords: Boros-Moll Polynomials, Real-rootedness, Sturm sequence, 3-log-concavity Download: PDF |