Asymptotics of Prolate Spheroidal Wave Functions
Classical Analysis and ODEs
2017-03-17 v3
Abstract
Uniform asymptotic approximations are obtained for the prolate spheroidal wave functions, in the high-frequency case. The results are obtained by an application of certain existing asymptotic solutions of differential equations, and involve elementary, Bessel, and parabolic cylinder functions. An asymptotic relationship between the prolate spheroidal equation separation parameter and the other parameters is also obtained, and error bounds are available for all approximations
Cite
@article{arxiv.1601.00699,
title = {Asymptotics of Prolate Spheroidal Wave Functions},
author = {T. M. Dunster},
journal= {arXiv preprint arXiv:1601.00699},
year = {2017}
}
Comments
Minor corrections and improvements. To appear in J. Class. Analysis