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  "body": "\n## Summary\n\nThe nome is the variable $q = e^{\\pi i\\tau}$ in which [[theta functions|2F5CYQJVAF]] and elliptic functions are expanded as power series.\nFor a real modulus $0 \u003c k \u003c 1$ it is $q = \\exp(-\\pi K'/K)$, where $K$ and $K'$ are [[complete elliptic integrals of the first kind|RM54CPPE12]].\nIt ties the modulus of the Jacobi elliptic functions to the period ratio of their lattice.\n\n## Explanations\n\n### L1 human\n\nElliptic functions depend on a shape parameter, which can be given as the modulus $k$ or as the ratio $\\tau$ of two periods.\nThe nome $q = e^{\\pi i\\tau}$ is a third way to give the same parameter, chosen so that series expansions are power series in $q$.\nFor moderate $k$, $q$ is very small, about $k^2/16$ when $k$ is small, so these series converge very fast.\nFor example, at $k = 1/\\sqrt2$ the nome is $e^{-\\pi} \\approx 0.0432$.\n",
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  "name": "Nome",
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  "source": "https://github.com/tamnd/math2/blob/main/nodes/YSA/YSAZVCZAZC.md",
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