Work

On a Transformation of Triple $q$-Series and Rogers-Hecke Type Series

Year: 2024

Type: article

Abstract: Using the method of the $q$-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 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.

Source: Symmetry Integrability and Geometry Methods and Applications

DOI: 10.3842/sigma.2024.086

Author: Zhi-Guo Liu

Institution: East China Normal University

Language: English

Topic: Advanced Mathematical Identities

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: diamond

Funders: National Natural Science Foundation of China, Science and Technology Commission of Shanghai Municipality

Awards: G1204540992, G1609915050, G7270659173