Bijective proofs of basic hypergeometric series identities (Q1099307)
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: Bijective proofs of basic hypergeometric series identities |
scientific article; zbMATH DE number 4040308
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Bijective proofs of basic hypergeometric series identities |
scientific article; zbMATH DE number 4040308 |
Statements
Bijective proofs of basic hypergeometric series identities (English)
0 references
1987
0 references
The authors give simple, completely bijective proofs of the \(q\)-binomial theorem and Heine's \({}_2\Phi_1\) transformation. Since all identities on basic hypergeometric series can be built out of these two fundamental identities, any basic hypergeometric identity can be proved bijectively, at least in theory, by building bijections out of these fundamental ones. The authors describe how this building process can be accomplished.
0 references
basic hypergeometric identity
0 references
\(q\)-binomial theorem
0 references
Heine's transformation
0 references
\(q\)-analogue of Gauss' theorem
0 references
\(q\)-analogue of Rummer's theorem
0 references
\(q\)-analogue of Saalschütz's theorem
0 references
very well poised evaluations
0 references
Watson's transformation
0 references
