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  "body": "\n## Summary\n\nThe log-gamma function is the logarithm of the [[gamma function|0H5SYBSED9]]: $\\ln\\Gamma(x)$ for real $x \u003e 0$, and its holomorphic extension $\\operatorname{Log}\\Gamma$ to the slit plane $\\C \\setminus (-\\infty, 0]$.\nIt is used because $\\Gamma$ grows faster than any exponential, so its logarithm is easier to compute and to estimate.\nIts derivative is the [[digamma function|HWRRXB0YXS]], and its asymptotic expansion is [[Stirling's series|K29QYWB6A5]].\n\n## Explanations\n\n### L1 human\n\nThe gamma function grows so fast that its values overflow quickly; for example $\\Gamma(171)$ is already larger than $10^{306}$.\nTaking the logarithm turns this huge growth into a gentle one, roughly like $x \\ln x$.\nProducts of gamma values become sums of log-gamma values, which is often simpler.\nFor example $\\ln\\Gamma(1) = \\ln\\Gamma(2) = 0$, and $\\ln\\Gamma(\\tfrac12) = \\tfrac12 \\ln \\pi$.\n",
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