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  "body": "\n## Summary\n\nThe dilogarithm is $\\operatorname{Li}_2(z) = \\sum_{k \\ge 1} \\frac{z^k}{k^2}$, the [[polylogarithm|96CHDZKGQ0]] of order $2$.\nIt equals $-\\int_0^z \\frac{\\ln(1 - u)}{u}\\, du$ and continues analytically to $\\C \\setminus [1, \\infty)$.\nIt satisfies remarkable functional equations, such as Euler's reflection formula and the [[five-term relation|6DHQTFAJ03]].\nIt appears in hyperbolic geometry, through the [[Bloch–Wigner function|Q8K5MWEXB9]], and in algebraic K-theory.\n\n## Explanations\n\n### L1 human\n\nThe dilogarithm is the next function after the logarithm in a natural chain: one divides by $u$ and integrates again.\nIt is not elementary, but it has many exact values.\nFor example, $\\operatorname{Li}_2(1) = \\frac{\\pi^2}{6}$ and $\\operatorname{Li}_2(-1) = -\\frac{\\pi^2}{12}$.\nIts identities, which relate values at points such as $z$, $1 - z$ and $1/z$, have made it a favourite of number theorists and physicists.\n",
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