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...
Збережено в:
| Опубліковано в: : | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Дата: | 2024 |
| Автор: | |
| Формат: | Стаття |
| Мова: | Англійська |
| Опубліковано: |
Інститут математики НАН України
2024
|
| Онлайн доступ: | https://nasplib.isofts.kiev.ua/handle/123456789/212609 |
| Теги: |
Додати тег
Немає тегів, Будьте першим, хто поставить тег для цього запису!
|
| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | On a Transformation of Triple -Series and Rogers-Hecke Type Series. Zhi-Guo Liu. SIGMA 20 (2024), 086, 37 pages |
Репозитарії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862712271905488896 |
|---|---|
| author | Liu, Zhi-Guo |
| author_facet | Liu, Zhi-Guo |
| citation_txt | On a Transformation of Triple -Series and Rogers-Hecke Type Series. Zhi-Guo Liu. SIGMA 20 (2024), 086, 37 pages |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
|
| first_indexed | 2026-03-19T18:13:08Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-212609 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2026-03-19T18:13:08Z |
| publishDate | 2024 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Liu, Zhi-Guo 2026-02-09T08:05:52Z 2024 On a Transformation of Triple -Series and Rogers-Hecke Type Series. Zhi-Guo Liu. SIGMA 20 (2024), 086, 37 pages 1815-0659 2020 Mathematics Subject Classification: 05A30; 33D05; 33D15; 32A05; 11E25; 32A10 arXiv:2401.14099 https://nasplib.isofts.kiev.ua/handle/123456789/212609 https://doi.org/10.3842/SIGMA.2024.086 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. I am grateful to the referees and the editors for proposing many very helpful comments and suggestions. I also thank Dandan Chen, Chun Wang, and Chang Xu for pointing out several misprints of an earlier version of this paper. This research is supported in part by the National Natural Science Foundation of China (Grant No. 12371328) and the Science and Technology Commission of Shanghai Municipality (No. 22DZ2229014). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On a Transformation of Triple -Series and Rogers-Hecke Type Series Article published earlier |
| spellingShingle | On a Transformation of Triple -Series and Rogers-Hecke Type Series Liu, Zhi-Guo |
| title | On a Transformation of Triple -Series and Rogers-Hecke Type Series |
| title_full | On a Transformation of Triple -Series and Rogers-Hecke Type Series |
| title_fullStr | On a Transformation of Triple -Series and Rogers-Hecke Type Series |
| title_full_unstemmed | On a Transformation of Triple -Series and Rogers-Hecke Type Series |
| title_short | On a Transformation of Triple -Series and Rogers-Hecke Type Series |
| title_sort | on a transformation of triple -series and rogers-hecke type series |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/212609 |
| work_keys_str_mv | AT liuzhiguo onatransformationoftripleseriesandrogershecketypeseries |