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, The Netherlands

Gil, A, Segura, J, & Temme, N.M. (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). doi:10.3842/SIGMA.2018.073