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The Boros-Moll polynomials Pm(a) arise in the evaluation of a quartic integral. It has been conjectured by Boros and Moll that these polynomials are infinitely log-concave. In this paper, we show that...
The Interlacing Log-concavity of the Boros-Moll Polynomials
interlacing log-concavity log-concavity the Boros-Moll polynomials
2014/6/3
We introduce the notion of interlacing log-concavity of a polynomial sequence {Pm(x)}m≥0, where Pm(x) is a polynomial of degree m with positive coefficients. This sequence is said to be interlacingly ...
Higher Order Log-Concavity in Euler's Difference Table
log-concavity 2-log-concavity reverse ultra log-concavity Euler's difference table
2014/6/3
For 0 ≤ k ≤ n, let ekn be the entries in Euler's difference table and let dkn = ekn/k!. Dumont and Randrianarivony showed ekn equals the number of permutations on [n] whose fixed points are contained ...
The Reverse Ultra Log-Concavity of the Boros-Moll Polynomials
log-concavity reverse ultra log-concavity Boros-Moll polynomials
2014/6/3
We prove the reverse ultra log-concavity of the Boros-Moll polynomials. We further establish an inequality which implies the log-concavity of the sequence {i!di(m)} for any m ≥ 2, where di(m) are the ...
On some properties of life distributions with increasing elasticity and log-concavity
Life distributions Log-concavity Closure property
2010/9/14
The purpose of this paper is to extend and systematize known results in log-concave and log-convex properties of life distributions. Also, to discuss the closure property of increasing generalized fai...