A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III
type: Item
instance of: scholarly article
title: A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III
zbMATH Open document ID: 0934.33021
author: Mizan Rahman
author: Sergei K. Suslov
published in: Methods and Applications of Analysis
publication date: 2000-04-10T00:00:00Z
review text: [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.
Mathematics Subject Classification ID: 33D05
Mathematics Subject Classification ID: 33D15
zbMATH DE Number: 1310571
zbMATH Keywords: Pearson-type equation
zbMATH Keywords: symmetric \(q\)-quadratic lattice
zbMATH Keywords: \(_6\Psi_6\) summation formulas
zbMATH Keywords: \(_8\Psi_8\) summation formulas
zbMATH Keywords: Barnes's type integrals
zbMATH Keywords: Ramanujan type integrals
zbMATH Keywords: non-terminating \(q\)-Jackson formula
zbMATH Keywords: Gosper's bilateral Jackson formula
reviewed by: P. K. Mital
MaRDI profile type: Publication
DOI: 10.4310/MAA.1998.V5.N4.A6
description: scientific article; zbMATH DE number 1310571