Consider the function $$f(x)=\ln \left\{\prod_{n=1}^{\infty}\left(\frac{1}{(-a^{n+1};a)_x}\right){(-a;a)_{\infty}}^x\right\}$$ where $(-a;a)_n$ is q-Pochhammer Symbol and $0<a<1$. Through my research I deal a functional sequence that $f$ is its limit function on $\mathbb{R^+}$. But my question is, can $f$ be simpler?Or Does $f$ have closed form? Thanks.
2026-03-26 22:16:09.1774563369
Can $f(x)=\ln \left\{\prod_{n=1}^{\infty}\left(\frac{1}{(-a^{n+1};a)_x}\right){(-a;a)_{\infty}}^x\right\}$ be simpler?
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