On the \(q\)-derivative and \(q\)-series expansions (Q2870232)
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: ON THE q-DERIVATIVE AND q-SERIES EXPANSIONS |
scientific article; zbMATH DE number 6247537
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the \(q\)-derivative and \(q\)-series expansions |
scientific article; zbMATH DE number 6247537 |
Statements
17 January 2014
0 references
\(q\)-series
0 references
\(q\)-derivative
0 references
Hecke-type series
0 references
sums of squares
0 references
\(q\)-Chu-Vandermonde summation
0 references
\(q\)-transformation formula
0 references
Andrews identity
0 references
Gauss identity
0 references
0 references
On the \(q\)-derivative and \(q\)-series expansions (English)
0 references
In this paper some nontrivial \(q\)-formulas involving many infinite products are derived using a general \(q\)-series expansion due to the author [Ramanujan J. 6, No. 4, 429--447 (2002; Zbl 1044.05012)]. These formulas include: a multitude of Hecke-type series identities (the well-known identity due to Andrews, Dyson and Hickerson, other identities of Andrews, some limiting cases of Watson's \(q\)-analog of Whipple's theorem), general formulas for sums of any number of squares and a new representation for the generating function for sums of three triangular numbers, which is slightly different from that of Andrews and also implies the famous result of Gauss that every integer is the sum of three triangular numbers.
0 references
