A q-Clausen-Orr type formula and its applications

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:453

Article

Guo, Hong-Fang^1,2  Guo, Victor J. W.²  Zeng, Jiang³ 

[1] East China Normal Univ, Dept Math, Shanghai 200241, Peoples R China

[2] Huaiyin Normal Univ, Sch Math Sci, Huaian 223300, Jiangsu, Peoples R China

[3] Univ Claude Bernard Lyon 1, CNRS, UMR 5208, Inst Camille Jordan, 43 Blvd 11 Novembre 1918, F-69622 Villeurbanne, France

关键词: q-Delannoy numbers;    q-analogue of Clausen's formula;    q-binomial theorem;    q-Chu-Vandermonde;    q-Pfaff-Saalschutz;   

DOI  :  10.1016/j.jmaa.2017.04.021

来源: Elsevier

【 摘 要 】

We show that certain terminating (6)phi(5) series can be factorized into a product of two (3)phi(2) series. As applications we prove a summation formula for a product of two q-Delannoy numbers along with some congruences for sums involving q-Delannoy numbers. This confirms three recent conjectures of the second author. (C) 2017 Elsevier Inc. All rights reserved.

【 授权许可】

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