# Product of a modified/generalized geometric progression

What is the solution to the following? It's sort of a modified/generalized geometric progression (or is there a known name for this kind?),

$$\lim_{N\to\infty}\prod_{n=0}^{N}(1+a^n), a\in(0,1)$$

• Try looking at Q-Pochhammer_symbol for some further inspiration. – Chinny84 Feb 4 '16 at 16:42
• So equation (53) of this page has the solution expressed in terms of Jacobi theta function, which I also need some time to understand. – Tian He Feb 5 '16 at 3:16