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A TRUNCATED IDENTITY OF EULER AND RELATED $q$-CONGRUENCES
Published online by Cambridge University Press: 08 April 2020
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Bulletin of the Australian Mathematical Society , Volume 102 , Issue 3 , December 2020 , pp. 353 - 359
- Copyright
- © 2020 Australian Mathematical Publishing Association Inc.
Footnotes
The first author was supported by the National Natural Science Foundation of China (grant 11801417).
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