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.

Jacobi polynomial, Laguerre polynomial, Large-beta asymptotics
dx.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