On a Transformation of Triple $q$-Series and Rogers-Hecke Type Series
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917795975921664 |
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| author | Liu, Zhi-Guo |
| author_facet | Liu, Zhi-Guo |
| contents | Using the method of the $q$-exponential differential operator, we give an extension of the Sears $_4ϕ_3$ transformation formula. Based on this extended formula and a $q$-series expansion formula for an analytic function around the origin, we present a transformation formula for triple $q$-series, which includes several interesting special cases, especially a double $q$-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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_14099 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On a Transformation of Triple $q$-Series and Rogers-Hecke Type Series Liu, Zhi-Guo Complex Variables Combinatorics Number Theory Quantum Algebra 05A30, 33D05, 33D15, 32A05, 11E25, 32A10 Using the method of the $q$-exponential differential operator, we give an extension of the Sears $_4ϕ_3$ transformation formula. Based on this extended formula and a $q$-series expansion formula for an analytic function around the origin, we present a transformation formula for triple $q$-series, which includes several interesting special cases, especially a double $q$-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. |
| title | On a Transformation of Triple $q$-Series and Rogers-Hecke Type Series |
| topic | Complex Variables Combinatorics Number Theory Quantum Algebra 05A30, 33D05, 33D15, 32A05, 11E25, 32A10 |
| url | https://arxiv.org/abs/2401.14099 |