Open Journal of Mathematical Analysis

Vol. 6 (2022), Issue 1, pp. 7 – 14
ISSN: 2616-8111 (Online) 2616-8103 (Print)
DOI: 10.30538/psrp-oma2022.0100

The \(q\)-Legendre inversions and balanced \(q\)-series identities

Xiaojing Chen\(^{1}\), and Wenchang Chu\(^{2,3,*}\)
\(^1\) School of Statistics, Qufu Normal University, Qufu (Shandong), China.
\(^{2}\) School of Mathematics and Statistics, Zhoukou Normal University (Henan), China.
\(^{3}\) Department of Mathematics and Physics, University of Salento, Lecce 73100, Italy.
Correspondence should be addressed to Wenchang Chu at chu.wenchang@unisalento.it

Copyright © 2022 Xiaojing Chen and Wenchang Chu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Received: October 7, 2021 – Accepted: December 5, 2021 – Published: June 21, 2022

Abstract

Two terminating balanced \(_4\phi_3\)-series identities are established by applying the bilateral \(q\)-Legendre inversions. Four variants of them are obtained by means of contiguous relations. According to the polynomial argument, four “dual” formulae for balanced \(_4\phi_3\)-series are deduced, that lead also to four non-terminating \(_2\phi_2\)-series identities.

Keywords:

keyword 1, keyword 2, keyword 3