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Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions

Authors:

Joris Van Deun,

Ronald CoolsAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 32, Issue 4

Pages 580 - 596

https://doi.org/10.1145/1186785.1186790

Published: 01 December 2006 Publication History

Abstract

We present an algorithm to compute integrals of the form ∫^∞₀ x^m ∏^k_i = 1J_{ν_i}(a_ix)dx with J_{ν_i}(x) the Bessel function of the first kind and (real) order ν_i. The parameter m is a real number such that ∑_i ν_i + m > −1 and the coefficients a_i are strictly positive real numbers. The main ingredients in this algorithm are the well-known asymptotic expansion for J_{ν_i}(x) and the observation that the infinite part of the integral can be approximated using the incomplete Gamma function Γ(a,z). Accurate error estimates are included in the algorithm, which is implemented as a MATLAB program.

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References

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Cited By

Lovat GCelozzi S(2025)Lucas decomposition and extrapolation methods for the evaluation of infinite integrals involving the product of three Bessel functions of arbitrary orderJournal of Computational and Applied Mathematics10.1016/j.cam.2024.116141453(116141)Online publication date: Jan-2025
https://doi.org/10.1016/j.cam.2024.116141
Lombardi GPapapicco D(2024)Quadrature of functions with endpoint singular and generalised polynomial behaviour in computational physicsComputer Physics Communications10.1016/j.cpc.2024.109124(109124)Online publication date: Feb-2024
https://doi.org/10.1016/j.cpc.2024.109124
Sugiura HHasegawa T(2021)A truncated Clenshaw-Curtis formula approximates integrals over a semi-infinite intervalNumerical Algorithms10.1007/s11075-020-00905-w86:2(659-674)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s11075-020-00905-w
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Index Terms

Algorithm 858: Computing infinite range integrals of an arbitrary product of Bessel functions
1. Mathematics of computing
  1. Mathematical analysis
    1. Numerical analysis
      1. Numerical differentiation
    2. Quadrature
  2. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 32, Issue 4

December 2006

145 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1186785

Issue’s Table of Contents

Copyright © 2006 ACM.

Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for components of this work owned by others than ACM must be honored. Abstracting with credit is permitted. To copy otherwise, or republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Request permissions from [email protected]

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Publication History

Published: 01 December 2006

Published in TOMS Volume 32, Issue 4

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Cited By

Lovat GCelozzi S(2025)Lucas decomposition and extrapolation methods for the evaluation of infinite integrals involving the product of three Bessel functions of arbitrary orderJournal of Computational and Applied Mathematics10.1016/j.cam.2024.116141453(116141)Online publication date: Jan-2025
https://doi.org/10.1016/j.cam.2024.116141
Lombardi GPapapicco D(2024)Quadrature of functions with endpoint singular and generalised polynomial behaviour in computational physicsComputer Physics Communications10.1016/j.cpc.2024.109124(109124)Online publication date: Feb-2024
https://doi.org/10.1016/j.cpc.2024.109124
Sugiura HHasegawa T(2021)A truncated Clenshaw-Curtis formula approximates integrals over a semi-infinite intervalNumerical Algorithms10.1007/s11075-020-00905-w86:2(659-674)Online publication date: 1-Feb-2021
https://dl.acm.org/doi/10.1007/s11075-020-00905-w
Oliveira e Silva DQuilodrán R(2020)Global maximizers for adjoint Fourier restriction inequalities on low dimensional spheresJournal of Functional Analysis10.1016/j.jfa.2020.108825(108825)Online publication date: Oct-2020
https://doi.org/10.1016/j.jfa.2020.108825
Ledder GZlotnik V(2017)Evaluation of oscillatory integrals for analytical groundwater flow and mass transport modelsAdvances in Water Resources10.1016/j.advwatres.2017.04.007104(284-292)Online publication date: Jun-2017
https://doi.org/10.1016/j.advwatres.2017.04.007
Bornemann F(2016)The SIAM 100-Digit Challenge: A Decade LaterJahresbericht der Deutschen Mathematiker-Vereinigung10.1365/s13291-016-0137-2118:2(87-123)Online publication date: 12-Apr-2016
https://doi.org/10.1365/s13291-016-0137-2
Ratnanather JKim JZhang SDavis ALucas S(2014)Algorithm 935ACM Transactions on Mathematical Software10.1145/250843540:2(1-12)Online publication date: 5-Mar-2014
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Golubovic RPolimeridis AMosig J(2013)The Weighted Averages Method for Semi-Infinite Range Integrals Involving Products of Bessel FunctionsIEEE Transactions on Antennas and Propagation10.1109/TAP.2013.228004861:11(5589-5596)Online publication date: Nov-2013
https://doi.org/10.1109/TAP.2013.2280048
Tröltzsch UWendler FKanoun O(2013)Simplified analytical inductance model for a single turn eddy current sensorSensors and Actuators A: Physical10.1016/j.sna.2012.11.024191(11-21)Online publication date: Mar-2013
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Mehrem R(2013)Analytical evaluation of an infinite integral over four spherical Bessel functionsApplied Mathematics and Computation10.1016/j.amc.2013.04.025219:21(10506-10509)Online publication date: 1-Jul-2013
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