Geodesic
Asymptotic Expansions of Jacobi Polynomials for Large Values of $\beta$ and of Their Zeros
Symmetry, integrability and geometry: methods and applications, Tome 14 (2018)

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Asymptotic approximations of Jacobi polynomials are given for large values of the $\beta$-parameter and of their zeros. The expansions are given in terms of Laguerre polynomials and of their zeros. The levels of accuracy of the approximations are verified by numerical examples.
Keywords: Jacobi polynomial; large-beta asymptotics; Laguerre polynomial. 
Amparo Gil; Javier Segura; Nico M. Temme. Asymptotic Expansions of Jacobi Polynomials for Large Values of $\beta$ and of Their Zeros. Symmetry, integrability and geometry: methods and applications, Tome 14 (2018). http://geodesic.mathdoc.fr/item/SIGMA_2018_14_a72/
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[1] Dimitrov D. K., dos Santos E. J. C., “Asymptotic behaviour of Jacobi polynomials and their zeros”, Proc. Amer. Math. Soc., 144 (2016), 535–545 | DOI | MR | Zbl

[2] Gil A., Segura J., Temme N. M., “Asymptotic approximations to the nodes and weights of Gauss–Hermite and Gauss–Laguerre quadratures”, Stud. Appl. Math., 140 (2018), 298–332, arXiv: 1709.09656 | DOI | MR | Zbl

[3] Gil A., Segura J., Temme N. M., Non-iterative computation of Gauss–Jacobi quadrature by asymptotic expansions for large degree, arXiv: 1804.07076

[4] Koornwinder T. H., Wong R., Koekoek R., Swarttouw R. F., “Orthogonal polynomials”, NIST Handbook of Mathematical Functions, U.S. Dept. Commerce, Washington, DC, 2010, 435–484 https://dlmf.nist.gov/18