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

Author(s): Xiaojing Chen1, Wenchang Chu2,3
1School of Statistics, Qufu Normal University, Qufu (Shandong), China.
2School of Mathematics and Statistics, Zhoukou Normal University (Henan), China.
3Department of Mathematics and Physics, University of Salento, Lecce 73100, Italy.
Copyright © Xiaojing Chen, 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.

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