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  "body": "\n## Summary\n\nThe Wilson polynomials $W_n(x^2; a, b, c, d)$ are orthogonal polynomials in the variable $x^2$ with four parameters, introduced by James Wilson in 1980.\nThey are given by terminating balanced ${}_4F_3$ hypergeometric series, and their weight on $(0, \\infty)$ is a ratio of products of [[gamma functions|0H5SYBSED9]].\nThey are at the top of the [[Askey scheme|RR2S05C09B]].\nEvery other family in the scheme arises from them, or from the [[Racah polynomials|P6JYNDX5DR]], by specialisation or limits.\nTheir $q$-analogues are the [[Askey–Wilson polynomials|RSNZNG0WA1]].\n\n## Explanations\n\n### L1 human\n\nThe classical orthogonal polynomials, such as those of Jacobi, Laguerre and Hermite, come in a few families with few parameters.\nThe Wilson polynomials are one family with four parameters from which all the others can be reached.\nSetting a parameter to a special value, or letting it go to infinity, moves down from the Wilson polynomials to the more familiar ones.\nThey are symmetric in their four parameters, which is not visible from the formula but is a deep identity.\n",
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