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  "body": "\n## Summary\n\nRamanujan's general theta function is $f(a, b) = \\sum_{n \\in \\Z} a^{n(n+1)/2} b^{n(n-1)/2}$ for complex $a, b$ with $\\abs{ab} \u003c 1$.\nIt is a two-variable form of the Jacobi [[theta function|2F5CYQJVAF]], symmetric in $a$ and $b$.\nBy the [[Jacobi triple product|JFP2DGMNXT]] it is an infinite product.\nIts special cases $\\varphi(q)$, $\\psi(q)$ and $f(-q)$ are the theta functions that Ramanujan used for partitions and modular equations.\n\n## Explanations\n\n### L1 human\n\nThe function $f(a, b)$ is a sum over all integers $n$, where positive $n$ mostly use powers of $a$ and negative $n$ mostly use powers of $b$.\nChoosing $a$ and $b$ as powers of one variable $q$ gives famous series.\nFor example, $f(q, q) = \\sum_{n \\in \\Z} q^{n^2} = 1 + 2q + 2q^4 + 2q^9 + \\cdots$, where each square $n^2 \u003e 0$ appears twice, once for $n$ and once for $-n$.\nIts square counts the ways to write a number as a sum of two squares.\n",
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