When did Jacobi prove the product formula for the discriminant function: $\Delta(\tau) = (2\pi)^{12}q\prod_{n \geq 1} (1 - q^n)^{24}$?

I have tried without success to track down references (other than looking through Jacobi's collected works), but when I search for terms like "Jacobi product" I get lots of hits on his triple product formula, and inserting "discriminant" into the search is not helping on isolating a reference that would discuss Jacobi's own work on this.

  • $\begingroup$ To the best of my knowledge,it was srinivasa ramanujan who first investigated the discriminant function,more especially its coefficients now known as ramanujan's tau function $\endgroup$ – Nicco Jul 26 '16 at 9:04
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    $\begingroup$ @Nicco, I was not asking about the Taylor coefficients, which of course were first studied closely by Ramanujan, but about the product formula that I wrote down. People like Weierstrass and Dedekind were surely familiar with this product from the study of elliptic/modular functions (cf. the Dedekind eta function). $\endgroup$ – KCd Jul 26 '16 at 14:23

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