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  "body": "\n## Summary\n\nThe K-function extends the hyperfactorial $1^1 \\cdot 2^2 \\cdots n^n$ to non-integer arguments.\nIt satisfies $K(1) = 1$ and $K(z + 1) = z^z K(z)$, so $K(n + 1) = 1^1 2^2 \\cdots n^n$ for positive integers $n$.\nIt is defined through an integral of $\\log \\Gamma$, where $\\Gamma$ is the [[gamma function|0H5SYBSED9]], and is related to the [[Barnes G-function|7E2JJWFF00]].\n\n## Explanations\n\n### L1 human\n\nThe factorial multiplies $1, 2, 3, \\ldots, n$.\nThe hyperfactorial multiplies $1^1, 2^2, 3^3, \\ldots, n^n$, so it grows even faster.\nThe K-function is a smooth curve through the values of the hyperfactorial, as the gamma function is a smooth curve through the factorials.\nFor example, $K(4) = 1^1 \\cdot 2^2 \\cdot 3^3 = 108$.\n",
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