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  "body": "\n## Summary\n\nThe Bessel polynomials $y_n$ are polynomials with positive integer coefficients that arise from the [[modified Bessel functions|2ET068BZZH]] of half-integer order.\nThey solve a second-order differential equation with polynomial coefficients.\nThey are orthogonal for a weight on a circle in the complex plane, not on an interval of the real line.\nTheir reversed forms are the denominators of Bessel filters in electrical engineering.\n\n## Explanations\n\n### L1 human\n\nBessel functions of half-integer order can be written with exponentials and finitely many powers of $1/x$.\nThe polynomials that appear in this way are the Bessel polynomials.\nThe first ones are $y_0 = 1$, $y_1 = 1 + x$ and $y_2 = 1 + 3x + 3x^2$.\nEngineers use them to design filters that delay all frequencies of a signal by almost the same time.\n",
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