1. On a transformation of triple $q$-series and Rogers--Hecke type series
- Author
-
Liu, Zhi-Guo
- Subjects
Mathematics - Complex Variables ,Mathematics - Combinatorics ,Mathematics - Number Theory ,Mathematics - Quantum Algebra ,05A30, 33D05, 33D15, 32A05, 11E25, 32A10 - Abstract
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
- Published
- 2024