Numerical evaluation of Bessel function integrals for functions with exponential dependence

J. L, H. H, R. P

Abstract


A numerical method for the calculation of Bessel function integrals is proposed for trial functions with exponential type behavior and evaluated for functions with and without explicit exponential dependence. This method utilizes the integral representation of the Bessel function to recast the problem as a double integral; one of which is calculated with Gauss-Chebyshev quadrature while the other uses a parameter-dependent Gauss-Laguerre quadrature in the complex plane. Accurate results can be obtained with relatively small orders of quadratures for the studied classes of functions.

Keywords


Bessel function integrals; Gaussian quadrature; Hankel transform; Gauss-Laguerre; Gauss-Chebyshev

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REVISTA MEXICANA DE FÍSICA E, year 18, issue 1, January-June 2021. Semiannual Journal published by Sociedad Mexicana de Física, A. C. Departamento de Física, 2º Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Apartado Postal 70-348. Tel. (+52)55-5622-4946, https://rmf.smf.mx/ojs/rmf-e, rmf@ciencias.unam.mx. Chief Editor: José Alejandro Ayala Mercado.  INDAUTOR Certificate of Reserve: 04-2019-080216402500-203, ISSN: 2683-2216 (on line), 1870-3542 (print), both granted by Instituto Nacional del Derecho de Autor.  Responsible for the last update of this issue, Technical Staff of Sociedad Mexicana de Física, A. C., Fís. Efraín Garrido Román, 2º. Piso, Facultad de Ciencias, Universidad Nacional Autónoma de México, Ciudad Universitaria, Alcaldía Coyacán, C.P. 04510 , Ciudad de México. Date of last modification, January 04, 2021.

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