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  "body": "\n## Summary\n\nThe Szász–Mirakyan operators approximate functions on the half-line $[0, \\infty)$ by series built from the [[Poisson distribution|0XB9GQTN9G]].\nThey play for $[0, \\infty)$ the role that [[Bernstein polynomials|0JT92VK307]] play for $[0, 1]$.\nThey are [[positive linear operators|AQDXWH4812]], so their convergence follows from Korovkin's theorem.\n\n## Explanations\n\n### L1 human\n\nTo approximate $f$ near a point $x \\ge 0$, sample $f$ at the grid points $k/n$.\nWeight the sample at $k/n$ by the probability that a Poisson random variable with mean $nx$ equals $k$.\nThe weights concentrate near $k/n \\approx x$ as $n$ grows, so the weighted average approaches $f(x)$.\nFor $f(t) = t$ the average is exactly $x$, because the Poisson variable has mean $nx$.\n",
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