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  "body": "\n## Summary\n\nThe reciprocal gamma function is the function $z \\mapsto 1/\\Gamma(z)$, where $\\Gamma$ is the [[gamma function|0H5SYBSED9]].\nBecause $\\Gamma$ has no zeros and only simple poles at $0, -1, -2, \\ldots$, the reciprocal is an [[entire function|0G4F0XB9X2]] with simple zeros exactly at these points.\nIt is often more convenient than $\\Gamma$ itself: it has an everywhere convergent [[Weierstrass product|53MZ2DGDTQ]] and a [[Hankel contour integral|2V0TG9Z3ZW]] valid for all $z$.\n\n## Explanations\n\n### L1 human\n\nThe gamma function has infinitely many points where it blows up.\nTurning it upside down, $1/\\Gamma$, changes these points into ordinary zeros, and the result is defined and smooth on the whole complex plane.\nFor example $1/\\Gamma(1) = 1$, $1/\\Gamma(\\tfrac12) = 1/\\sqrt{\\pi}$, and $1/\\Gamma(0) = 0$.\nOn the positive real axis it starts at $0$, rises to a maximum between $1$ and $2$, and then decays very fast, like one over a factorial.\n",
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