Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros

• Published in: Symmetry, Integrability and Geometry: Methods and Applications
• Date: 2018
• Main Authors: Gil, A., Segura, J., Temme, N.M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2018
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/209777
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Asymptotic Expansions of Jacobi Polynomials for Large Values of β and of Their Zeros / A. Gil, J. Segura, N.M. Temme // Symmetry, Integrability and Geometry: Methods and Applications. — 2018. — Т. 14. — Бібліогр.: 4 назв. — англ.

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.