10 research outputs found

    The qq-log-convexity of Domb's polynomials

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    In this paper, we prove the qq-log-convexity of Domb's polynomials, which was conjectured by Sun in the study of Ramanujan-Sato type series for powers of π\pi. As a result, we obtain the log-convexity of Domb's numbers. Our proof is based on the qq-log-convexity of Narayana polynomials of type BB and a criterion for determining qq-log-convexity of self-reciprocal polynomials.Comment: arXiv admin note: substantial text overlap with arXiv:1308.273

    On the qq-log-convexity conjecture of Sun

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    In his study of Ramanujan-Sato type series for 1/π1/\pi, Sun introduced a sequence of polynomials Sn(q)S_n(q) as given by Sn(q)=k=0n(nk)(2kk)(2(nk)nk)qk,S_n(q)=\sum\limits_{k=0}^n{n\choose k}{2k\choose k}{2(n-k)\choose n-k}q^k, and he conjectured that the polynomials Sn(q)S_n(q) are qq-log-convex. By imitating a result of Liu and Wang on generating new qq-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the qq-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture

    On the Modes of Polynomials Derived from Nondecreasing Sequences

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    Wang and Yeh proved that i