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  "body": "\n## Summary\n\nThe Askey scheme is a chart that organises the hypergeometric orthogonal polynomials into levels connected by limit relations.\nAt the top are the [[Wilson|1CPF7SWQ3S]] and [[Racah polynomials|P6JYNDX5DR]], given by ${}_4F_3$ series; at the bottom are the [[Hermite polynomials|MGACY98E9H]].\nEach arrow says that one family is a limit of another as a parameter tends to a special value or to infinity.\nIt shows the classical families of Jacobi, Laguerre and Hermite as degenerations of a few very general ones.\n\n## Explanations\n\n### L1 human\n\nThere are many named families of orthogonal polynomials, and at first they look unrelated.\nThe Askey scheme is a family tree for them.\nFamilies with more parameters are higher up, and moving down an arrow means fixing or removing a parameter by a limit.\nFor example, the [[Krawtchouk polynomials|CJGKW80KBR]] for $N$ coin tosses with probability $a/N$ become the [[Charlier polynomials|6KH8KVYS3R]] as $N \\to \\infty$, just as the binomial distribution becomes the Poisson distribution.\n",
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