Dataset of Bessel function [Formula: see text] maxima and minima to 600 orders and 10000 extrema

Nicholas A Mecholsky; Sepideh Akhbarifar; Werner Lutze; Marek Brandys; Ian L Pegg

doi:10.1016/j.dib.2021.107508

Dataset of Bessel function $J_{n}$ maxima and minima to 600 orders and 10000 extrema

Data Brief. 2021 Oct 30:39:107508. doi: 10.1016/j.dib.2021.107508. eCollection 2021 Dec.

Authors

Nicholas A Mecholsky^{1

2}, Sepideh Akhbarifar^{1

2}, Werner Lutze^{1

2}, Marek Brandys^{1

2}, Ian L Pegg^{1

2}

Affiliations

¹ Vitreous State Laboratory, United States.
² Department of Physics, The Catholic University of America, 620 Michigan Ave NE, Washington, D.C. 20064, United States.

Abstract

Bessel functions of the first kind are ubiquitous in the sciences and engineering in solutions to cylindrical problems including electrostatics, heat flow, and the Schrödinger equation. The roots of the Bessel functions are often quoted and calculated, but the maxima and minima for each Bessel function, used to match Neumann boundary conditions, have not had the same treatment. Here we compute 10000 extrema for the first 600 orders of the Bessel function $J$ . To do this, we employ an adaptive root solver bounded by the roots of the Bessel function and solve to an accuracy of $10^{- 19}$ . We compare with the existing literature (to 30 orders and 5 maxima and minima) and the results match exactly. It is hoped that these data provide values needed for orthogonal function expansions and numerical expressions including the calculation of geometric correction factors in the measurement of resistivity of materials, as is done in the original paper using these data.

Keywords: Bessel functions; Extrema; GCF; Maximum; Minimum.