Asymptotic approximations of Jacobi polynomials are given for large values of the β-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.

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doi.org/10.3842/SIGMA.2018.073
Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Gil, A., Segura, J., & Temme, N. (2018). Asymptotic expansions of Jacobi polynomials for large values of β and of their zeros. Symmetry, Integrability and Geometry: Methods and Applications (SIGMA), 14, 073:1–073:9. doi:10.3842/SIGMA.2018.073