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  "body": "\n## Summary\n\nThe $q$-Pochhammer symbol $(a; q)_n = (1 - a)(1 - aq) \\cdots (1 - aq^{n-1})$ is a $q$-analogue of the rising factorial.\nIts infinite version $(a; q)_\\infty$ is a convergent [[infinite product|JYV1Y8XX16]] for $\\abs{q} \u003c 1$.\nIt is the basic building block of $q$-series, basic hypergeometric series and generating functions for integer partitions.\nThe exact definition is in [[q-Pochhammer symbol|K8PHD2NAW9]].\n\n## Explanations\n\n### L1 human\n\nThe $q$-Pochhammer symbol is a product of factors $1 - a$, $1 - aq$, $1 - aq^2$, and so on, each with one more power of $q$.\nFor example, $(q; q)_3 = (1 - q)(1 - q^2)(1 - q^3)$.\nSuch products appear when one counts partitions of integers: the coefficients of $1/(q; q)_\\infty$, expanded in powers of $q$, are the partition numbers.\n",
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