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Article overview
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On the $q$-log-convexity conjecture of Sun | Donna Q.J. Dou
; Anne X.Y. Ren
; | Date: |
13 Aug 2013 | Abstract: | In his study of Ramanujan-Sato type series for $1/pi$, Sun introduced a
sequence of polynomials $S_n(q)$ as given by
$$S_n(q)=sumlimits_{k=0}^n{nchoose k}{2kchoose k}{2(n-k)choose n-k}q^k,$$
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. | Source: | arXiv, 1308.2736 | Services: | Forum | Review | PDF | Favorites |
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