On the qq-log-convexity conjecture of Sun


In his study of Ramanujan-Sato type series for 1/Ο€1/\pi, Sun introduced a sequence of polynomials Sn(q)S_n(q) as given by Sn(q)=βˆ‘k=0n(nk)(2kk)(2(nβˆ’k)nβˆ’k)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

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