research-article

Algorithm 877: A Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument

Author:

Masao KodamaAuthors Info & Claims

ACM Transactions on Mathematical Software (TOMS), Volume 34, Issue 4

Article No.: 22, Pages 1 - 21

https://doi.org/10.1145/1377596.1377602

Published: 01 July 2008 Publication History

Abstract

The algorithm presented provides a package of subroutines for calculating the cylindrical functions J_ν(x), N_ν(x), H_ν⁽¹⁾(x), H_ν⁽²⁾(x) where the order ν is complex and the real argument x is nonnegative. The algorithm is written in Fortran 95 and calculates the functions using single, double, or quadruple precision according to the value of a parameter defined in the algorithm. The methods of calculating the functions are based on a series expansion, Debye's asymptotic expansions, Olver's asymptotic expansions, and recurrence methods (Miller's algorithms). The relative errors of the functional values computed by this algorithm using double precision are less than 2.4×10^− 13 in the region 0 ≤ Re ν ≤ 64, 0 ≤ Im ν ≤ 63, 0.024 ≤ x ≤ 97.

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Software for A Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument

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References

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Cited By

Rosa G(2023)An Accurate and Numerically Stable Formulation for Computing the Electromagnetic Fields in Uniform Bend Rectangular WaveguidesIEEE Transactions on Microwave Theory and Techniques10.1109/TMTT.2022.321983071:3(988-996)Online publication date: Mar-2023
https://doi.org/10.1109/TMTT.2022.3219830
Gill NStarrett C(2017)Tartarus: A relativistic Green’s function quantum average atom codeHigh Energy Density Physics10.1016/j.hedp.2017.06.00224(33-38)Online publication date: Sep-2017
https://doi.org/10.1016/j.hedp.2017.06.002
Torres JBaptista AMachado V(2013)Coupling Analysis in Concentric Ring WaveguidesJournal of Lightwave Technology10.1109/JLT.2013.226363331:13(2140-2145)Online publication date: Jul-2013
https://doi.org/10.1109/JLT.2013.2263633
Show More Cited By

Index Terms

Algorithm 877: A Subroutine Package for Cylindrical Functions of Complex Order and Nonnegative Argument
1. Mathematics of computing
  1. Mathematical software

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Published In

cover image ACM Transactions on Mathematical Software

ACM Transactions on Mathematical Software Volume 34, Issue 4

July 2008

152 pages

ISSN:0098-3500

EISSN:1557-7295

DOI:10.1145/1377596

Issue’s Table of Contents

Copyright © 2008 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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Association for Computing Machinery

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Publication History

Published: 01 July 2008

Accepted: 01 June 2007

Revised: 01 June 2007

Received: 01 March 2006

Published in TOMS Volume 34, Issue 4

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Cited By

Rosa G(2023)An Accurate and Numerically Stable Formulation for Computing the Electromagnetic Fields in Uniform Bend Rectangular WaveguidesIEEE Transactions on Microwave Theory and Techniques10.1109/TMTT.2022.321983071:3(988-996)Online publication date: Mar-2023
https://doi.org/10.1109/TMTT.2022.3219830
Gill NStarrett C(2017)Tartarus: A relativistic Green’s function quantum average atom codeHigh Energy Density Physics10.1016/j.hedp.2017.06.00224(33-38)Online publication date: Sep-2017
https://doi.org/10.1016/j.hedp.2017.06.002
Torres JBaptista AMachado V(2013)Coupling Analysis in Concentric Ring WaveguidesJournal of Lightwave Technology10.1109/JLT.2013.226363331:13(2140-2145)Online publication date: Jul-2013
https://doi.org/10.1109/JLT.2013.2263633
Kodama M(2011)Algorithm 912ACM Transactions on Mathematical Software (TOMS)10.1145/1916461.191647137:4(1-25)Online publication date: 1-Feb-2011
https://dl.acm.org/doi/10.1145/1916461.1916471
Gil ASegura JTemme N(2011)Basic Methods for Computing Special FunctionsRecent Advances in Computational and Applied Mathematics10.1007/978-90-481-9981-5_4(67-121)Online publication date: 2011
https://doi.org/10.1007/978-90-481-9981-5_4

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