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What are the definition domains for $n$ and $x$ that gives $x^{(n)}$ (upper pochhammer symbol) and $(x)_n$ (lower pochhammer symbol) in $\mathbb{R}$ ?

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Normally I'd assume $x\in\mathbb C$ and $n\in\{0,1,2,3,\ldots\}$ (and the values of both expressions are $1$ when $n=0$). But I wouldn't be surprise if someone's used non-integer values of $n$, but maybe it would take some work to figure out what the right definition should be.

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