%0 Journal Article
%T A New Transformation Formula for 2¦×2
%A WANG Xiang-li
%A WEI Zan-qing
%A LIU Dong-fang
%J Journal of Chongqing Normal University
%D 2012
%I Chongqing Normal University
%X Many bilateral basic hypergeometric series can be derived from unilateral basic hypergeometric series, in this paper, we study the nonterminating unilateral basic hypergeometric series shifting into bilateral basic hypergeometric series. Firstly,using the bilateral extension method, we derive a new transformation formula between bilateral basic hypergeometric series 2¦×2 and unilateral basic hypergeometric series 21 through the nonterminating form of the q-Saalsch¨¹z formula. Secondly, we also deduce another transformation formula between bilateral basic hypergeometric series 2¦×2 and unilateral basic hypergeometric series 21 by using the Heine¡¯s 21 transformation formula to the 21 series in theory 1. Finally, we give a new proof of the nonterminating extension of the q-Saalsch¨¹z formula by taking special value f=q in theory 1.
%K q-series£» nonterminating form of the q-Saalsch¨¹z formula£» nonterminating form of the q-Vandermonde formula£» Heine¡¯s 21 transformation formula
%U http://journal.cqnu.edu.cn/1206/pdf/120611.pdf