Some applications of Gasper's bibasic summation
The main result is the bibasic summation formula \[ \begin{multlined} \sum_{k=0}^n(-1)^k\frac{(1-d)(1-ad/b)(1-ad^2q^{2k}/b)}{(1-dq^k)(1-adq^k/b)}\, \\ \times \frac{(ad^2/b;q)_k(adq^k;p)_n(b/dq^k;p)_n}{(q;q)_k(q;q)_{n-k}(ad^2/b;q)_{n+k+1}} \,q^{k(k+1)/2} =\frac{(a;p)_n(b;p)_n}{(dq;q)_n(adq/b;q)_n}, \end{multlined} \] where the \(q\)-shifted factorial is defined by \((a;q)_n=\prod_{j=0}^{n-1}(1-aq^j)\), and its applications to basic hypergeometric series. Another bibasic summation formula, announced in the introduction as equation~(3.5), is not given in the paper.
scientific article; zbMATH DE number 5541241
scientific article