Amparo Gil, Javier Segura, Nico M. Temme, “Asymptotic Expansions of Jacobi Polynomials for Large Values of <nobr>$\beta$</nobr> and of Their Zeros”, SIGMA, 2018, Volume 14,073, 9 pp.

This article is cited in 2 papers

Asymptotic Expansions of Jacobi Polynomials for Large Values of $\beta$ and of Their Zeros

Amparo Gil^a, Javier Segura^a, Nico M. Temme^b

^a Universidad de Cantabria, 39005-Santander, Spain
^b IAA, 1825 BD 25, Alkmaar, The Netherlands
Former address: Centrum Wiskunde & Informatica (CWI), Science Park 123, 1098 XG Amsterdam, The Netherlands

Abstract: Asymptotic approximations of Jacobi polynomials are given for large values of the $\beta$-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.

Keywords: Jacobi polynomial; large-beta asymptotics; Laguerre polynomial.

MSC: 33C45; 41A60; 65D20

Received: April 19, 2018; in final form July 12, 2018; Published online July 17, 2018

Language: English

DOI: 10.3842/SIGMA.2018.073