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.
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The research of the second author was supported by Academic Research Fund R146000027112 from the National University of Singapore.
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Kongsiriwong, S., Liu, ZG. Uniform proofs of q-Series-product identities. Results. Math. 44, 312–339 (2003). https://doi.org/10.1007/BF03322989
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DOI: https://doi.org/10.1007/BF03322989