A TRUNCATED IDENTITY OF EULER AND RELATED q-CONGRUENCES
A TRUNCATED IDENTITY OF EULER AND RELATED q-CONGRUENCES
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欧拉的截断恒等式和相关的 q 同余
DOI：
10.1017/s0004972720000301
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发表时间：
2020-12-01
影响因子：
0.7
通讯作者：
Huang, Zhong-Yu
中科院分区：
文献类型：
--
作者：
Liu, JI-Cai;Huang, Zhong-Yu
讨论了欧拉截断恒等式，并给出了它的一个组合证明。我们也推出了两个有限恒等式作为推论。作为应用，我们建立了q-加泰罗尼亚数和的两个相关的q-同余，其中一个已被Tauraso[‘一些涉及加泰罗尼亚数的q-类似物’，ad . Appl]证明。数学学报，48(2012),603-614]。
We discuss a truncated identity of Euler and present a combinatorial proof of it. We also derive two finite identities as corollaries. As an application, we establish two related q-congruences for sums of q-Catalan numbers, one of which has been proved by Tauraso ['q-Analogs of some congruences involving Catalan numbers', Adv. Appl. Math. 48 (2012), 603-614] by a different method.