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  "body": "\n## Summary\n\nThe elliptic gamma function $\\Gamma(z; p, q)$ is a two-parameter generalisation of the [[q-gamma function|68P2VKSEP5]].\nIt is a double infinite product, and shifting $z$ to $qz$ multiplies it by a theta function in the base $p$.\nIn this way it stands to theta functions as the gamma function stands to linear functions.\nIt is the basic object of elliptic hypergeometric series and integrals.\n\n## Explanations\n\n### L1 human\n\nThe gamma function turns multiplication by $x$ into a shift: $\\Gamma(x + 1) = x\\, \\Gamma(x)$.\nThe $q$-gamma function does the same with $q$-numbers in place of $x$.\nThe elliptic gamma function goes one step further and uses theta functions, which are infinite products with a second parameter $p$.\nWhen $p = 0$ the theta function becomes the simple factor $1 - z$ and the theory falls back to the $q$-world.\n",
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