Branden's Conjectures on the Boros-Moll Polynomials

William Y. C. Chen; Donna Q. J. Dou; Arthur L. B. Yang

Branden's Conjectures on the Boros-Moll Polynomials

Combinatorics 2012-05-03 v1 Classical Analysis and ODEs

Authors: William Y. C. Chen , Donna Q. J. Dou , Arthur L. B. Yang

Abstract

We prove two conjectures of Br\"{a}nd\'{e}n 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 $P_n(x)$ .

Keywords

conjectures and proofs

Cite

@article{arxiv.1205.0305,
  title  = {Branden's Conjectures on the Boros-Moll Polynomials},
  author = {William Y. C. Chen and Donna Q. J. Dou and Arthur L. B. Yang},
  journal= {arXiv preprint arXiv:1205.0305},
  year   = {2012}
}

Comments

8 pages

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