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.
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.