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  "body": "\n## Summary\n\nThe Neville theta functions $\\theta_s$, $\\theta_c$, $\\theta_d$, $\\theta_n$ are rescaled Jacobi [[theta functions|2F5CYQJVAF]].\nTheir argument is the argument $u$ of the [[Jacobi elliptic functions|P071B692JF]].\nWith this normalisation the Jacobi functions are simple quotients: $\\operatorname{sn} = \\theta_s/\\theta_n$, $\\operatorname{cn} = \\theta_c/\\theta_n$ and $\\operatorname{dn} = \\theta_d/\\theta_n$.\nThe letters $s, c, d, n$ match the letters in the names of the twelve Jacobi functions, so any Jacobi function $\\operatorname{pq}$ is $\\theta_p/\\theta_q$.\n\n## Explanations\n\n### L1 human\n\nTheta functions are fast-converging series, and the Jacobi elliptic functions are ratios of them.\nIn the classical form the theta functions use a rescaled angle $\\pi u/(2K)$ and carry awkward constant factors.\nNeville chose the scaling so that the constants disappear from the ratios.\nThen, for example, $\\operatorname{sd} u = \\theta_s(u)/\\theta_d(u)$, read directly from the letters.\n",
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