Expression for a double product of exponential functions

Question

I would like to obtain a nice analytic expression for $$ \prod_{i=1}^n\prod_{j=1}^k (1-e^{-x_{ij}}), $$ where $0<x_{ij}<1$. I saw something similar in the link https://math.stackexchange.com/a/3138951/725141, but I am not sure if it's possible to extend this result. What I mean by "nice" is basically to get rid of the products.

Answer 1

You can rewrite as a single product,

$$\prod_{l=1}^{nk}(1-e^{-x_l})$$ with the re-indexing $l=i+n(j-1)$.

Note that the solution given in the linked question is just the expansion of the product and is in fact more complicated than the original product.