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  "body": "\n## Summary\n\nThe little $q$-Jacobi polynomials $p_n(x; a, b \\mid q)$ are a family of orthogonal polynomials defined by a terminating [[basic hypergeometric series|EB4N9RQR51]].\nThey are orthogonal for a discrete weight carried by the points $q^k$ with $k = 0, 1, 2, \\ldots$.\nAs $q \\to 1$ with $a = q^\\alpha$ and $b = q^\\beta$, they tend to the [[Jacobi polynomials|TRD7DSF2KR]] in a shifted variable.\nThey belong to the $q$-analogue of the [[Askey scheme|RR2S05C09B]].\n\n## Explanations\n\n### L1 human\n\nOrdinary Jacobi polynomials are orthogonal for an integral over an interval.\nIn the little $q$-Jacobi family the integral is replaced by a sum over the points $1, q, q^2, \\ldots$, which pile up at $0$.\nThe parameter $q$ between $0$ and $1$ controls how dense these points are.\nThe first nontrivial member is the linear polynomial $p_1(x) = 1 - \\frac{1 - abq^2}{1 - aq} x$.\nLetting $q$ approach $1$ fills the gaps between the points and gives back the classical Jacobi polynomials.\n",
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