A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III
[For part II see the review above (Zbl 0934.33020).] In this paper the authors have first obtained the summation formulas for the bilateral very-well-poised \(_6\Psi_6\) series from a Pearson-type difference equation on a symmetric \(q\)-quadratic lattice without the benefit of any transformation formula or other summation formulas. Next, this formula is used to obtain a formula for the very-well-poised, balanced \(_8\Psi_8\) series which has the non-terminating \(q\)-Jackson formula and Gosper's bilateral Jackson formula as special cases.
scientific article; zbMATH DE number 1310571