Analytic aspects of generalized central trinomial coefficients
Analytic aspects of generalized central trinomial coefficients
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DOI：
10.1016/j.jmaa.2023.127424
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发表时间：
2023-03
影响因子：
1.3
通讯作者：
Huyile Liang;Yaling Wang;Yi Wang
中科院分区：
文献类型：
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作者：
Huyile Liang;Yaling Wang;Yi Wang
通常的和广义的中心三项式系数的整除性和同余性已经得到了广泛的研究。本论文致力于这些数字的分析性质。我们证明了中心三项多项式Tn（x）只有真实的根，Tn（x）的根与Tn + 1（x）的根以及Tn + 2（x）的根交错，从而肯定地回答了菲斯克的一个公开问题.建立了广义中心三项式系数Tn（B，c）构成对数凸序列或Stieltjes矩序列的充要条件.
The divisibility and congruence of usual and generalized central trinomial coefficients have been extensively investigated. The present paper is devoted to analytic properties of these numbers. We show that usual central trinomial polynomials T n (x) have only real roots, and roots of T n (x) interlace those of T n+ 1 (x), as well as those of T n+ 2 (x), which gives an affirmative answer to an open question of Fisk. We establish necessary and sufficient conditions such that the generalized central trinomial coefficients T n (b, c) form a log-convex sequence or a Stieltjes moment sequence.