Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema

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 funct...

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Autores principales:	Nicholas A. Mecholsky, Sepideh Akhbarifar, Werner Lutze, Marek Brandys, Ian L. Pegg
Formato:	article
Lenguaje:	EN
Publicado:	Elsevier 2021
Materias:	Bessel functions GCF Extrema Minimum Maximum Computer applications to medicine. Medical informatics R858-859.7 Science (General) Q1-390
Acceso en línea:	https://doaj.org/article/1be162d529b045b88c64ce8da4862c38
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spelling	oai:doaj.org-article:1be162d529b045b88c64ce8da4862c382021-11-06T04:30:23ZDataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema2352-340910.1016/j.dib.2021.107508https://doaj.org/article/1be162d529b045b88c64ce8da4862c382021-12-01T00:00:00Zhttp://www.sciencedirect.com/science/article/pii/S2352340921007782https://doaj.org/toc/2352-3409Bessel 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.Nicholas A. MecholskySepideh AkhbarifarWerner LutzeMarek BrandysIan L. PeggElsevierarticleBessel functionsGCFExtremaMinimumMaximumComputer applications to medicine. Medical informaticsR858-859.7Science (General)Q1-390ENData in Brief, Vol 39, Iss , Pp 107508- (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Bessel functions GCF Extrema Minimum Maximum Computer applications to medicine. Medical informatics R858-859.7 Science (General) Q1-390
spellingShingle	Bessel functions GCF Extrema Minimum Maximum Computer applications to medicine. Medical informatics R858-859.7 Science (General) Q1-390 Nicholas A. Mecholsky Sepideh Akhbarifar Werner Lutze Marek Brandys Ian L. Pegg Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema
description	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.
format	article
author	Nicholas A. Mecholsky Sepideh Akhbarifar Werner Lutze Marek Brandys Ian L. Pegg
author_facet	Nicholas A. Mecholsky Sepideh Akhbarifar Werner Lutze Marek Brandys Ian L. Pegg
author_sort	Nicholas A. Mecholsky
title	Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema
title_short	Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema
title_full	Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema
title_fullStr	Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema
title_full_unstemmed	Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema
title_sort	dataset of bessel function jn maxima and minima to 600 orders and 10000 extrema
publisher	Elsevier
publishDate	2021
url	https://doaj.org/article/1be162d529b045b88c64ce8da4862c38
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Dataset of Bessel function Jn maxima and minima to 600 orders and 10000 extrema

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