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Is there a way to express a closed formula for the finite product: $$\prod_{n=1}^{N}(an-b)$$ Maybe it can be done through the Pochhammer symbol?

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We can start by taking out a factor of $a^N$, leaving us with $a^N \prod_{n=1}^{N} (n-\frac{b}{a})$, and now we can just use the Pochhammer symbol(I'll assume you know what this is as you mention it in your question) to get $a^N(1-\frac{b}{a})_{N}$

It is known that $(x)_{N} = \frac{\Gamma(x+n)}{\Gamma(x)}$(this should be intuitively obvious from the definition), so our closed form is $\boxed{a^N \frac{\Gamma(1-\frac{b}{a}+N)}{\Gamma(1-\frac{b}{a})}}$

I'm not a hundred percent sure that a nicer form doesn't exist, but this is the best that I could come up with.

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