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.

Additional Metadata
Keywords Jacobi polynomial, Laguerre polynomial, Large-beta asymptotics
Persistent URL dx.doi.org/10.3842/SIGMA.2018.073
Journal Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
Citation
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