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  "body": "\n## Summary\n\nThe Racah polynomials are a finite family of orthogonal polynomials, given by terminating balanced ${}_4F_3$ hypergeometric series.\nThey are polynomials in the quadratic variable $\\lambda(x) = x(x + \\gamma + \\delta + 1)$, orthogonal for a weight on the points $x = 0, 1, \\dots, N$.\nThey sit at the top of the [[Askey scheme|RR2S05C09B]] together with the [[Wilson polynomials|1CPF7SWQ3S]].\nThey are named after Giulio Racah because the [[6-j symbols|D17XX5N9VF]] of quantum angular momentum can be written in terms of them.\n\n## Explanations\n\n### L1 human\n\nIn the Askey scheme, families of orthogonal polynomials are arranged by how many parameters they have.\nThe Racah polynomials are the discrete family with the most parameters, four of them.\nThe other discrete families, such as the Hahn, Krawtchouk and Charlier polynomials, arise from them by letting parameters go to limits.\nIn physics they appear when three quantum angular momenta are added in two different orders.\n",
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