The 2-log-convexity of the Apery Numbers
The 2-log-convexity of the Apery Numbers
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DOI：
10.1090/s0002-9939-2010-10575-0
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发表时间：
2009-12
期刊：
影响因子：
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通讯作者：
William Y. C. Chen;Ernest X. W. Xia
中科院分区：
文献类型：
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作者：
William Y. C. Chen;Ernest X. W. Xia
给出了一种证明满足三项递归关系的序列的2-对数凸性的方法。我们证明了Apery数、Cohen-Rhin数、Motzkin数、Fine数、3阶和4阶Franel数以及大Schroder数都是2-对数凸的。数值证据表明，所有这些序列对任何$k\geq 1$都是k-对数凸的，可能除了开始项的数目不变外。
We present an approach to proving the 2-log-convexity of sequences satisfying three-term recurrence relations. We show that the Apery numbers, the Cohen-Rhin numbers, the Motzkin numbers, the Fine numbers, the Franel numbers of order 3 and 4 and the large Schroder numbers are all 2-log-convex. Numerical evidence suggests that all these sequences are k-log-convex for any $k\geq 1$ possibly except for a constant number of terms at the beginning.