A note on an identity of Andrews
In this paper, starting from an identity of \textit{G. E. Andrews} [Adv. Math. 41, 137--172 (1981; Zbl 0477.33001)] and using the \(q\)-exponential operator technique, the author derives , for \(0<| q| <1\), the following identity: \[ d\sum_{n=0}^{\infty}{\left(q/bc,q/ce,acdf;q\right)_n\over \left(ad,df;q\right)_{n+1} \left(q^2/bcde;q\right)_n}q^n- c\sum_{n=0}^{\infty}{\left(q/bd,q/de,acdf;q\right)_n\over \left(ac,cf;q\right)_{n+1} \left(q^2/bcde;q\right)_n}q^n \] \[ \qquad\qquad=d{\left(q,qd/c,c/d,abcd,acdf,bcdf,acde,cdef,bcde/q;q\right)_\infty\over \left(ac,ad,cf,df,bc,bd,ce,de,abc^2d^2ef/q;q\right)_\infty}. \]
scientific article; zbMATH DE number 2161322