The Bessel zeta function-Reference-Cited by-同舟云学术

The Bessel zeta function

Published:2022-08-01 Issue:8 Volume:63 Page:083504
ISSN:0022-2488
Container-title:Journal of Mathematical Physics
language:en
Short-container-title:J. Math. Phys.

Author:

Naber M. G.¹^ORCID,Bruck B. M.²^ORCID,Costello S. E.³^ORCID

Affiliation:

1. Department of Science and Mathematics, Monroe County Community College, 1555 S. Raisinville Rd., Monroe, Michigan 48161-9746, USA

2. Department of Mathematics and Statistics, University of Toledo, 2801 W. Bancroft St., Toledo, Ohio 43606, USA

3. Department of Physics, University of Toledo, 2801 W. Bancroft St., Toledo, Ohio 43606, USA

Abstract

Two representations of the Bessel zeta function are investigated. An incomplete representation is constructed using contour integration and an integral representation due to Hawkins is fully evaluated (analytically continued) to produce two infinite series. This new representation, evaluated at integer values of the argument, produces results that are consistent with known results (values, slope, and pole structure). Not surprisingly, the two representations studied are found to have similar coefficients but a slightly different functional form. A representation of the Riemann zeta function is obtained by allowing the order of the Bessel function to go to 1/2.

Publisher

AIP Publishing

Subject

Mathematical Physics,Statistical and Nonlinear Physics

Link

https://aip.scitation.org/doi/pdf/10.1063/5.0105399

Reference18 articles.

1. J. Hawkins, “On a Zeta function associated with Bessel’s equation,” Ph.D. thesis, University of Illinois, 1983.

2. The zeta function constructed from the zeros of the Bessel function

3. Sum rules for zeros of Bessel functions and an application to spherical Aharonov-Bohm quantum bags

4. Zeta function of the Bessel operator on the negative real axis