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  "body": "\n## Summary\n\nThe incomplete gamma functions split the integral of the [[gamma function|0H5SYBSED9]] at a point $x$.\nThe lower one $\\gamma(s, x)$ integrates $t^{s-1} e^{-t}$ from $0$ to $x$, and the upper one $\\Gamma(s, x)$ integrates it from $x$ to $\\infty$.\nTheir sum is $\\Gamma(s)$.\nThey give the distribution function of the [[gamma distribution|0B80PAQD3C]] and contain the [[exponential integral|EV6ZDQ0NDY]] and the [[error function|7Y56QCZSZJ]] as special cases.\n\n## Explanations\n\n### L1 human\n\nThe gamma function is the area under the curve $t^{s-1} e^{-t}$ on the whole positive half line.\nCut this area at a point $x$.\nThe part on the left is the lower incomplete gamma function, and the part on the right is the upper one.\nFor $s = 1$ the curve is $e^{-t}$, and the two parts are $1 - e^{-x}$ and $e^{-x}$.\n",
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