A semi-finite proof of Jacobi's triple product identity
Jun-Ming Zhu
TL;DR
This paper provides an elementary semi-finite proof of Jacobi's triple product identity using Euler's q-exponential functions, simplifying the understanding of this classical mathematical result.
Contribution
It introduces a new semi-finite proof method for Jacobi's triple product identity based on Euler's q-exponential functions, offering a simpler approach.
Findings
Elementary proof of Jacobi's triple product identity
Utilizes Euler's q-exponential functions for proof
Simplifies understanding of the classical identity
Abstract
Jacobi's triple product identity is proved from one of Euler's -exponential functions in an elementary way.
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Taxonomy
TopicsAdvanced Mathematical Identities · Mathematical functions and polynomials · Advanced Combinatorial Mathematics