Identities and Properties of Multi-Dimensional Generalized Bessel Functions
Abstract
The Generalized Bessel Function (GBF) extends the single variable Bessel function to several dimensions and indices in a nontrivial manner. Two-dimensional GBFs have been studied extensively in the literature and have found application in laser physics, crystallography, and electromagnetics. In this article, we document several properties of -dimensional GBFs including an underlying partial differential equation structure, asymptotics for simultaneously large order and argument, and analysis of generalized Neumann, Kapteyn, and Schl\"{o}milch series. We extend these results to mixed-type GBFs where appropriate.
Cite
@article{arxiv.1908.11683,
title = {Identities and Properties of Multi-Dimensional Generalized Bessel Functions},
author = {Parker Kuklinski and David A. Hague},
journal= {arXiv preprint arXiv:1908.11683},
year = {2021}
}
Comments
Revised version of manuscript. Updated references. Paper will not be submitted to journal, but will remain here on arXiv as a reference