A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III (Q1293929)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III |
scientific article; zbMATH DE number 1310571
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III |
scientific article; zbMATH DE number 1310571 |
Statements
A unified approach to the summation and integration formulas for \(q\)-hypergeometric functions. III (English)
0 references
10 April 2000
0 references
[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.
0 references
Pearson-type equation
0 references
symmetric \(q\)-quadratic lattice
0 references
\(_6\Psi_6\) summation formulas
0 references
\(_8\Psi_8\) summation formulas
0 references
Barnes's type integrals
0 references
Ramanujan type integrals
0 references
non-terminating \(q\)-Jackson formula
0 references
Gosper's bilateral Jackson formula
0 references
