Work

Asymptotic Bessel-function expansions for Legendre and Jacobi functions

Year: 2019

Type: article

Abstract: We present new asymptotic series for the Legendre and Jacobi functions of the first and second kinds in terms of Bessel functions with appropriate arguments. The results are useful in the context of scattering problems, improve on known limiting results, and allow the calculation of corrections to the leading Bessel-function approximations for these functions. Our derivations of these series are based on Barnes-type representations of the Legendre, Jacobi, and Bessel functions; our method appears to be new. We use the results, finally, to obtain asymptotic Bessel function expansions for the rotation functions needed to describe the scattering of particles with spin.

Source: Journal of Mathematical Physics

DOI: 10.1063/1.5030869

Author: Loyal Durand

Institution: University of Wisconsin–Madison

Language: English

Topic: Mathematical functions and polynomials

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funder: National Science Foundation

Award: Programs on Critical Problems in Physics, Astrophysics and Biophysics at the Aspen Center for Physics