Zeros of Bessel cross-products coming from oblique derivative boundary value problems
Classical Analysis and ODEs
2019-09-04 v1 Spectral Theory
Abstract
The paper is devoted to (combinations of) Bessel cross-products that arise from oblique derivative boundary value problems for the Laplacian in a circular annulus. We show that like their Neumann-Laplacian counterpart (and unlike the Dirichlet-Laplacian), they possess two kinds of zeros: those that can be derived by McMahon series and diverge to infinity in the limit, and exceptional ones that remain finite. For both cases we find asymptotic expressions for a fixed oblique angle and vanishing thickness of the annulus. We further present plots of numerically computed zeros and discuss their behaviour when the oblique angle changes and the thickness remains fixed.
Keywords
Cite
@article{arxiv.1909.00293,
title = {Zeros of Bessel cross-products coming from oblique derivative boundary value problems},
author = {Stanislav Budzinskiy},
journal= {arXiv preprint arXiv:1909.00293},
year = {2019}
}
Comments
11 pages, 3 figures