تقرير
On a transformation of triple $q$-series and Rogers--Hecke type series
| العنوان: | On a transformation of triple $q$-series and Rogers--Hecke type series |
|---|---|
| المؤلفون: | Liu, Zhi-Guo |
| سنة النشر: | 2024 |
| المجموعة: | Mathematics |
| مصطلحات موضوعية: | Mathematics - Complex Variables, Mathematics - Combinatorics, Mathematics - Number Theory, Mathematics - Quantum Algebra, 05A30, 33D05, 33D15, 32A05, 11E25, 32A10 |
| الوصف: | Using the method of $q$-exponential differential operator we give an extension of the Sears $_4\phi_3$ 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 application of this transformation formula to Rogers--Hecke type series are discussed. More than 100 Rogers--Hecke type identities including Andrews's identities for the sums of three squares and the sums of three triangular numbers are obtained. Comment: 41pages |
| نوع الوثيقة: | Working Paper |
| URL الوصول: | http://arxiv.org/abs/2401.14099 |
| رقم الأكسشن: | edsarx.2401.14099 |
| قاعدة البيانات: | arXiv |
| الوصف غير متاح. |