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a different normalisation. comment-normalisation: This table uses the DLMF normalisation CITE{DLMFRepresentation}.- The Wikipedia article CITE{Wiki} writes a different sign convention for the two- upper parameters that contain the variable.+ The Wikipedia article CITE{Wiki} writes the upper parameters as $a\pm t$ rather+ than $a\pm ix$, so its $p_n(z)$ is $W_n(-z;a,b,c,d)$ here. Tags: - polynomial
title: 'DLMF 18.26.1: Wilson polynomial hypergeometric representation' url: https://dlmf.nist.gov/18.26.E1- DLMFConstraints:- title: 'DLMF Table 18.25.1: Wilson-class variables and parameter constraints'- url: https://dlmf.nist.gov/18.25.T1 DLMFJacobiLimit: title: 'DLMF 18.26.7: Wilson-Jacobi limit'
complete: 'no' complete-note: it holds every nondecreasing quadruple with $a,b,c,d\in\{\tfrac12,1,\tfrac32,2,3\}$- and every degree $0\leq n\leq10$; the nondecreasing order uses the shape-parameter- symmetry to avoid repeated entries+ and every degree $0\leq n\leq10$; these five shape values give a compact grid+ of small integral and half-integral cases whose entries block stays below about+ half the soft limit rigour details: 'The generator computes the terminating hypergeometric sum in Sage''s rational polynomial ring $\mathbb{Q}[y]$, with every division made in $\mathbb{Q}$. - Before the draft was filled, all entries were checked for exactness and measured- by `agents/table-build/dry_run.py`: it found 770 entries, longest 450 characters,- and a 141.3 KB entries block. The generator checked symmetry in $a,b,c,d$, the- special value $W_n(-r^2)$ for each shape parameter $r$, the leading coefficient,- and the exact Wilson-Jacobi limit in CITE{DLMFJacobiLimit}.+ The generator checked symmetry in $a,b,c,d$, the special value $W_n(-r^2)$ for+ each shape parameter $r$, the leading coefficient, and the exact Wilson-Jacobi+ limit in CITE{DLMFJacobiLimit}. '
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