On the q-log-convexity conjecture of Sun

2013/08/13 by Donna Q. J. Dou, Dou, Donna Q. J., Anne X. Y. Ren +1 · 1 citation
Mathematics · #Combinatorics (math.CO) #FOS: Mathematics #math.CO

paper · pdf · doi:10.48550/arxiv.1308.2736

arxiv created 2013/08/15 · arxiv updated 2013/08/16

Abstract

In his study of Ramanujan-Sato type series for 1/π, Sun introduced a sequence of polynomials S_n(q) as given by S_n(q)=∑_k=0ⁿn\choose k2k\choose k2(n-k)\choose n-kq^k, and he conjectured that the polynomials S_n(q) are q-log-convex. By imitating a result of Liu and Wang on generating new q-log-convex sequences of polynomials from old ones, we obtain a sufficient condition for determining the q-log-convexity of self-reciprocal polynomials. Based on this criterion, we then give an affirmative answer to Sun's conjecture.

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