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  "body": "\n## Summary\n\nThe $q$-gamma function $\\Gamma_q$ is a [[q-analog|GFSDMJHHVA]] of the [[gamma function|0H5SYBSED9]].\nIt is a quotient of two [[q-Pochhammer symbols|Y1X8ZZQ7VM]] and satisfies $\\Gamma_q(x + 1) = [x]_q\\, \\Gamma_q(x)$, where $[x]_q = \\frac{1 - q^x}{1 - q}$ is the $q$-number.\nAs $q \\to 1^-$ it tends to $\\Gamma(x)$.\nIt appears throughout the theory of basic hypergeometric series.\n\n## Explanations\n\n### L1 human\n\nIn $q$-analogs, a number $n$ is replaced by $[n]_q = 1 + q + \\cdots + q^{n-1}$, which becomes $n$ again when $q = 1$.\nThe $q$-factorial is then $[1]_q [2]_q \\cdots [n]_q$.\nThe $q$-gamma function fills in this $q$-factorial between the whole numbers, as the gamma function does for the factorial.\nFor example, $\\Gamma_q(3) = [2]_q = 1 + q$, which is $2 = 2!$ when $q = 1$.\n",
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