Uniform proofs of q-Series-product identities |
| |
Authors: | Sarachai Kongsiriwong Zhi-Guo Liu |
| |
Institution: | 1. Department of Mathematics, University of Illinois, 1409 W. Green St., Urbana, IL, 61801 2. Department of Mathematics, East China Normal University, Shanghai, 200062, P. R. China
|
| |
Abstract: | In this paper we give a simple proof of the Jacobi triple product identity by using basic properties of cube roots of unity. Then we give a new proof of the quintuple product identity, the septuple product identity and Winquist’s identity by using the Jacobi triple product identity and basic properties of cube and fifth roots of unity. Furthermore, we derive some new product identities by this uniform method. Later, we give some generalizations of those identities. Lastly, we derive some modular equations. |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|