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A TRUNCATED IDENTITY OF EULER AND RELATED -CONGRUENCES
Bulletin of the Australian Mathematical Society ( IF 0.7 ) Pub Date : 2020-04-08 , DOI: 10.1017/s0004972720000301
JI-CAI LIU , ZHONG-YU HUANG

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.

中文翻译:

欧拉的截断恒等式和相关的同余

我们讨论了欧拉的截断恒等式并给出了它的组合证明。我们还推导出两个有限恒等式作为推论。作为一个应用程序,我们建立了两个相关的$q$- 总和的全等$q$- 加泰罗尼亚数,其中之一已被 Tauraso 证明 ['$q$- 涉及加泰罗尼亚数字的一些同余的类比,进阶。应用程序。数学。 48(2012), 603–614] 采用不同的方法。
更新日期:2020-04-08
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