What are specific proofs of Jacobi Triple Product Identity?

Question

I am looking for the Special Proofs. Here is a reference from MSE. Motivation for/history of Jacobi's triple product identity

I also know that a simple proof via Functional Equation from the book of An Invitation to q-series Hei-Chi-Chan. it has a very nice explanation , step by step. I also have learnt that Zeilberg's recursive proof.

What are the other interesting proofs about this identity you know? ? Thanks for your answers.

I find the proof by Jacobi in Fundamenta Nova to be much simpler and elegant. I have presented the same in my blog post. — Paramanand Singh, Jul 02 '20 at 04:02

score 2 · Accepted Answer · edited Jul 15 '23 at 08:14

2

For a combinatorial proof of Jacobi's Triple Identity see the article by Kolitsch.

For an elementary number-theoretic proof see the article by Herbert S. Wilf, which also has references for other proofs.

For a standard proof see for example here.

Another well-known proof is by Andrews, using Euler's identities.

edited Jul 15 '23 at 08:14

The Amplitwist

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answered Jun 26 '20 at 12:06

Dietrich Burde

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that's a great answer. thanks:) – user1062 Jun 26 '20 at 12:08

What are specific proofs of Jacobi Triple Product Identity?

1 Answers1