On a Transformation of Triple -Series and Rogers-Hecke Type Series - Liu, Zhi-Guo (Symmetry, Integrability and Geometry: Methods and Applications, 2024)
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.