Amparo Gil, Javier Segura, Nico M. Temme, “McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions”, SIGMA, 2024, Volume 20,075, 9 pp.

McMahon-Type Asymptotic Expansions of the Zeros of the Coulomb Wave Functions

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

^a Universidad de Cantabria, 39005 Santander, Spain
^b Valkenierstraat 25, 1825BD Alkmaar, The Netherlands

Abstract: We derive asymptotic expansions of the large zeros of the Coulomb wave functions and for those of their derivatives. The new expansions have the same form as the McMahon expansions of the zeros of the Bessel functions and reduce to them when a parameter is equal to zero. Numerical tests are provided to demonstrate the accuracy of the expansions.

Keywords: Coulomb wave functions, McMahon-type zeros, asymptotic expansions.

MSC: 33C47, 33C10, 33C15, 41A60, 65D20, 65H05

Received: February 23, 2024; in final form August 7, 2024; Published online August 10, 2024

Language: English

DOI: 10.3842/SIGMA.2024.075