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  "body": "\n## Summary\n\nThe Pochhammer symbol $(a)_n$ is the rising factorial $a (a + 1) \\cdots (a + n - 1)$, a product of $n$ consecutive terms that go up by $1$ starting at $a$.\nIt is the basic building block of the [[hypergeometric series|428M453CR2]], whose coefficients are quotients of Pochhammer symbols.\nFor $a$ not a non-positive integer it equals $\\Gamma(a + n)/\\Gamma(a)$, which ties it to the [[gamma function|0H5SYBSED9]].\nIn combinatorics the same notation $(x)_n$ often stands for the [[falling factorial|0SJNCJCCQG]] instead, so one has to check the convention of each text.\n\n## Explanations\n\n### L1 human\n\nThe [[factorial|0XWG0JGDFW]] $n!$ multiplies $1, 2, \\ldots, n$.\nThe Pochhammer symbol does the same but may start at any number $a$: it multiplies $a, a + 1, \\ldots$ for $n$ steps.\nFor example $(3)_2 = 3 \\cdot 4 = 12$ and $(\\tfrac12)_2 = \\tfrac12 \\cdot \\tfrac32 = \\tfrac34$.\nStarting at $a = 1$ gives back the factorial: $(1)_n = n!$.\n",
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