The reverse ultra log-concavity of the Boros-Moll polynomials
نویسندگان
چکیده
منابع مشابه
The Reverse Ultra Log-Concavity of the Boros-Moll Polynomials
Based on the recurrence relations on the coefficients of the Boros-Moll polynomials Pm(a) = ∑ i di(m)a i derived independently by Kauers and Paule, and Moll, we are led to the discovery of the reverse ultra log-concavity of the sequence {di(m)}. We also show that the sequence {i!di(m)} is log-concave for m ≥ 1. Two conjectures are proposed.
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Let [Formula: see text] be a triangular array of numbers. We say that [Formula: see text] is skew log-concave if for any fixed n, the sequence [Formula: see text] is log-concave. In this paper, we show that the Boros-Moll sequences are almost skew log-concave.
متن کاملThe Concavity and Convexity of the Boros-Moll Sequences
In their study of a quartic integral, Boros and Moll discovered a special class of sequences, which is called the Boros–Moll sequences. In this paper, we consider the concavity and convexity of the Boros–Moll sequences {di(m)}i=0. We show that for any integer m > 6, there exist two positive integers t0(m) and t1(m) such that di(m)+di+2(m) > 2di+1(m) for i ∈ [0, t0(m)] ⋃ [t1(m),m−2] and di(m)+di...
متن کاملBrändén’s Conjectures on the Boros-Moll Polynomials
We prove two conjectures of Brändén on the real-rootedness of the polynomials Qn(x) and Rn(x) which are related to the Boros-Moll polynomials Pn(x). In fact, we show that both Qn(x) and Rn(x) form Sturm sequences. The first conjecture implies the 2-log-concavity of Pn(x), and the second conjecture implies the 3-log-concavity of Pn(x). AMS Classification 2010: Primary 26C10; Secondary 05A20, 30C15.
متن کاملThe ratio monotonicity of the Boros-Moll polynomials
In their study of a quartic integral, Boros and Moll discovered a special class of Jacobi polynomials, which we call the Boros-Moll polynomials. Kauers and Paule proved the conjecture of Moll that these polynomials are logconcave. In this paper, we show that the Boros-Moll polynomials possess the ratio monotone property which implies the log-concavity and the spiral property. We conclude with a...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 2009
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-09-09976-6