Two generalized q -exponential operators and their applications

Advances in Difference Equations

Wei Tan¹  Nadia Na Li¹ 

[1] School of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, P.R. China

关键词: q-series;    q-exponential operator;    q-integral;    q-Chu-Vandermonde sums;    Askey-Wilson integral;    33D15;    05A15;   

DOI  :  10.1186/s13662-016-0741-6

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

In this paper, we construct two generalized q-exponential operators with three parameters and obtain some operator identities. As applications, we give two formal extensions of the q-Gauss sum. An extension of the q-Chu-Vandermonde sums is also obtained by the operator technique. In addition, we also deduce a formal extension of the Askey-Wilson integral and a formal extension of Sears’ two-term summation formula. Meanwhile, some curious q-series identities are derived.

【 授权许可】

CC BY