On a Transformation of Triple -Series and Rogers-Hecke Type Series
Using the method of the q-exponential differential operator, we give an extension of the Sears ₄₃ transformation formula. Based on this extended formula and a -series expansion formula for an analytic function around the origin, we present a transformation formula for triple -series, which includes...
Gespeichert in:
| Veröffentlicht in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Datum: | 2024 |
| 1. Verfasser: | |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Інститут математики НАН України
2024
|
| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/212609 |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | On a Transformation of Triple -Series and Rogers-Hecke Type Series. Zhi-Guo Liu. SIGMA 20 (2024), 086, 37 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Zusammenfassung: | Using the method of the q-exponential differential operator, we give an extension of the Sears ₄₃ transformation formula. Based on this extended formula and a -series expansion formula for an analytic function around the origin, we present a transformation formula for triple -series, which includes several interesting special cases, especially a double -series summation formula. Some applications of this transformation formula to Rogers-Hecke type series are discussed. More than 100 Rogers-Hecke type identities, including Andrews' identities for the sums of three squares and the sums of three triangular numbers, are obtained.
|
|---|---|
| ISSN: | 1815-0659 |