{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T07:16:29Z","timestamp":1783667789645,"version":"3.55.0"},"reference-count":60,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2027,1,1]],"date-time":"2027-01-01T00:00:00Z","timestamp":1798761600000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,6,28]],"date-time":"2026-06-28T00:00:00Z","timestamp":1782604800000},"content-version":"vor","delay-in-days":0,"URL":"http:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100000923","name":"Australian Research Council","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100000923","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/501100015894","name":"ARC Centre of Excellence for Mathematical & Statistical Frontiers","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100015894","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Journal of Computational and Applied Mathematics"],"published-print":{"date-parts":[[2027,1]]},"DOI":"10.1016\/j.cam.2026.117915","type":"journal-article","created":{"date-parts":[[2026,6,27]],"date-time":"2026-06-27T23:01:51Z","timestamp":1782601311000},"page":"117915","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"C","title":["Finite precision computation of the polylogarithm function for complex parameters and arguments"],"prefix":"10.1016","volume":"489","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7882-7329","authenticated-orcid":false,"given":"Matthew","family":"Roughan","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"key":"10.1016\/j.cam.2026.117915_bib0001","series-title":"Frontiers in Number Theory, Physics, and Geometry II","first-page":"3","author":"Zagier","year":"2007"},{"key":"10.1016\/j.cam.2026.117915_bib0002","doi-asserted-by":"crossref","first-page":"2807","DOI":"10.1098\/rspa.2003.1156","article-title":"The dilogarithm function for complex argument","author":"Maximon","year":"2003","journal-title":"Proc. R. Soc. Lond. A."},{"key":"10.1016\/j.cam.2026.117915_bib0003","doi-asserted-by":"crossref","first-page":"3909","DOI":"10.1103\/PhysRevE.56.3909","article-title":"Polylogarithms and Riemann\u2019s \u03b6 function","volume":"56","author":"Lee","year":"1997","journal-title":"Phys. Rev. E"},{"key":"10.1016\/j.cam.2026.117915_bib0004","series-title":"An Introduction to Hypergeometric Functions","author":"Duverney","year":"2020"},{"key":"10.1016\/j.cam.2026.117915_bib0005","doi-asserted-by":"crossref","first-page":"678","DOI":"10.1103\/PhysRev.83.678","article-title":"Note on the Bose-Einstein integral functions","volume":"83","author":"Robinson","year":"1951","journal-title":"Phys. Rev."},{"key":"10.1016\/j.cam.2026.117915_bib0006","series-title":"Technical Report","article-title":"The Computation of Polylogarithms","author":"Wood","year":"1992"},{"key":"10.1016\/j.cam.2026.117915_bib0007","series-title":"Polylogarithms and associated functions","author":"Lewin","year":"1981"},{"issue":"1","key":"10.1016\/j.cam.2026.117915_bib0008","doi-asserted-by":"crossref","first-page":"169","DOI":"10.1112\/plms\/s2-4.1.169","article-title":"On function sum theorems connected with the series","volume":"s2-4","author":"Rogers","year":"1907","journal-title":"Proc. Lond. Math. Soc."},{"key":"10.1016\/j.cam.2026.117915_bib0009","doi-asserted-by":"crossref","unstructured":"A.G. Bytsko, Two-term dilogarithm identities related to conformal field theory, 1999. arXiv:math-ph\/9911012 [math-ph].","DOI":"10.1023\/A:1007618823700"},{"key":"10.1016\/j.cam.2026.117915_bib0010","doi-asserted-by":"crossref","unstructured":"A.N. Kirillov, Dilogarithm identities and spectra in conformal field theory, 1992. arXiv:hep-th\/9211137 [hep-th].","DOI":"10.1007\/978-1-4899-1612-9_8"},{"key":"10.1016\/j.cam.2026.117915_bib0011","series-title":"33Rd IEEE International Conference on Microelectronics (MIEL)","first-page":"1","article-title":"Recent applications of polylogarithms in MOSFET modeling","author":"Ortiz-Conde","year":"2023"},{"issue":"130","key":"10.1016\/j.cam.2026.117915_bib0012","first-page":"582","article-title":"Complex zeros of the Jonqui\u00e8re or polylogarithm function","volume":"29","author":"Fornberg","year":"1975","journal-title":"Math. Comput."},{"key":"10.1016\/j.cam.2026.117915_bib0013","doi-asserted-by":"crossref","first-page":"581","DOI":"10.1007\/BF01932969","article-title":"On the numerical calculation of polylogarithms","volume":"12","author":"Jacobs","year":"1972","journal-title":"BIT Numer. Math."},{"issue":"4","key":"10.1016\/j.cam.2026.117915_bib0014","doi-asserted-by":"crossref","DOI":"10.1145\/360715.360722","article-title":"Algorithm 490: the dilogarithm function of a real argument [S22]","volume":"18","author":"Ginsberg","year":"1975","journal-title":"Commun. ACM"},{"issue":"1","key":"10.1016\/j.cam.2026.117915_bib0015","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1016\/S0010-4655(03)00294-7","article-title":"On the evaluation of generalized Bose-Einstein and Fermi-Dirac integrals","volume":"155","author":"Bhagat","year":"2003","journal-title":"Comput. Phys. Commun."},{"key":"10.1016\/j.cam.2026.117915_bib0016","unstructured":"R.E. Crandall, Note on fast polylogarithm computation, 2006. https:\/\/www.reed.edu\/physics\/faculty\/crandall\/papers\/Polylog.pdf, accessed Oct 28th, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0017","doi-asserted-by":"crossref","first-page":"211","DOI":"10.1007\/s11075-007-9153-8","article-title":"An efficient algorithm for accelerating the convergence of oscillatory series, useful for computing the polylogarithm and Hurwitz zeta functions","volume":"47","author":"Vepstas","year":"2008","journal-title":"Numer. Algorithms"},{"key":"10.1016\/j.cam.2026.117915_bib0018","article-title":"Unified algorithms for polylogarithm, l-series, and zeta variants","author":"Crandall","year":"2012","journal-title":"Algorithmic Reflect.: Sel. Works"},{"key":"10.1016\/j.cam.2026.117915_bib0019","doi-asserted-by":"crossref","first-page":"115","DOI":"10.1016\/j.jat.2014.10.004","article-title":"Computation and theory of Mordell-Tornheim-Witten sums II","volume":"197","author":"Bailey","year":"2015","journal-title":"J. Approx. Theory"},{"key":"10.1016\/j.cam.2026.117915_bib0020","first-page":"462","article-title":"Crandall\u2019s computation of the incomplete Gamma function and the Hurwitz zeta function, with applications to Dirichlet l-series","volume":"268","author":"Bailey","year":"2015","journal-title":"Appl. Math. Comput."},{"key":"10.1016\/j.cam.2026.117915_bib0021","unstructured":"polylogPython, Polylogarithms and Clausen functions, mpmath 1.1.0, Python 3.6.9. http:\/\/mpmath.org\/doc\/current\/functions\/zeta.html#polylogarithms-and-clausen-functions."},{"key":"10.1016\/j.cam.2026.117915_bib0022","unstructured":"polyl_wolfr_languag_system, Polylog, Wolfram Language & System. https:\/\/reference.wolfram.com\/language\/ref\/PolyLog.html."},{"key":"10.1016\/j.cam.2026.117915_bib0023","unstructured":"L. Vepstas, Anant \u2013 Algorithmic \u2019n Analytic Number Theory, Version 0.2.4, 2019. https:\/\/github.com\/linas\/anant."},{"issue":"754\u20132008","key":"10.1016\/j.cam.2026.117915_bib0024","first-page":"1","article-title":"IEEE Standard for floating-Point arithmetic","year":"2008","journal-title":"IEEE Stand."},{"issue":"1","key":"10.1016\/j.cam.2026.117915_bib0025","doi-asserted-by":"crossref","first-page":"65","DOI":"10.1137\/141000671","article-title":"Julia: a fresh approach to numerical computing","volume":"59","author":"Bezanson","year":"2017","journal-title":"SIAM Rev."},{"key":"10.1016\/j.cam.2026.117915_bib0026","article-title":"Man creates one programming language to rule them all","author":"Finley","year":"2014","journal-title":"WIRED"},{"key":"10.1016\/j.cam.2026.117915_bib0027","unstructured":"M. Roughan, The Polylogarithm Function in Julia, 2020. arXiv: 2010.09860 [math.NA]."},{"key":"10.1016\/j.cam.2026.117915_bib0028","series-title":"Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables","author":"Abramowitz","year":"1964"},{"key":"10.1016\/j.cam.2026.117915_bib0029","series-title":"NIST Digital Library of Mathematical Functions","year":"2025"},{"issue":"3\/4","key":"10.1016\/j.cam.2026.117915_bib0030","doi-asserted-by":"crossref","first-page":"161","DOI":"10.6028\/jres.076B.012","article-title":"The Stieltjes constants","volume":"76B","author":"Liang","year":"1972","journal-title":"J. Res. Natl. Bur. Stand. \u2013 Math. Sci."},{"key":"10.1016\/j.cam.2026.117915_bib0031","unstructured":"oeis, The On-Line Encyclopedia of Integer Sequences (OEIS), https:\/\/oeis.org\/."},{"key":"10.1016\/j.cam.2026.117915_bib0032","doi-asserted-by":"crossref","first-page":"338","DOI":"10.1016\/j.cam.2008.07.040","article-title":"An efficient algorithm for the Hurwitz zeta and related functions","volume":"225","author":"Coffey","year":"2009","journal-title":"J. Comput. Appl. Math."},{"issue":"146","key":"10.1016\/j.cam.2026.117915_bib0033","doi-asserted-by":"crossref","first-page":"778","DOI":"10.1090\/S0025-5718-1979-0521291-X","article-title":"The dilogarithm function of a real argument","volume":"33","author":"Morris","year":"1979","journal-title":"Math. Comput."},{"key":"10.1016\/j.cam.2026.117915_bib0034","doi-asserted-by":"crossref","first-page":"93","DOI":"10.1007\/BF00692071","article-title":"Numerical evaluation of the dilogarithm of complex argument","volume":"62","author":"Os\u00e1car","year":"1995","journal-title":"Celest. Mech. Dyn. Astron."},{"key":"10.1016\/j.cam.2026.117915_bib0035","doi-asserted-by":"crossref","first-page":"233","DOI":"10.1016\/0010-4655(93)90093-R","article-title":"On the computation of generalized Fermi-Dirac and Bose-Einstein integrals","volume":"74","author":"Gautschi","year":"1993","journal-title":"Comput. Phys. Commun."},{"issue":"02","key":"10.1016\/j.cam.2026.117915_bib0036","doi-asserted-by":"crossref","first-page":"135","DOI":"10.1142\/S2810939223500028","article-title":"Simplifying polylogarithms with machine learning","volume":"01","author":"Dersy","year":"2023","journal-title":"Int. J. Data Sci. Math. Sci."},{"key":"10.1016\/j.cam.2026.117915_bib0037","unstructured":"A. Voigt, polylogarithm, 2025(GitHub codea). https:\/\/github.com\/Expander\/polylogarithm, accessed Oct 22nd, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0038","unstructured":"A. Voigt, PolyLog.jl, 2025b, (Julia packageb). https:\/\/github.com\/Expander\/PolyLog.jl, accessed Oct 22nd, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0039","unstructured":"A. Voigt, polylog.rs, 2025c, (GitHub codec). https:\/\/github.com\/Expander\/polylog.rs, accessed Oct 22nd, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0040","unstructured":"S.L. Moshier, Cephes, 2025, (GitHub). https:\/\/github.com\/jeremybarnes\/cephes, accessed Oct 22nd, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0041","unstructured":"F. Johansson, W. Hart, D. Harvey, S. Pancratz, T. Bachmann, M. Hansen, D. Schultz, A. Novocin, FLINT: Fast Library for Number Theory, 2025, (Software package). https:\/\/flintlib.org\/doc\/polylogarithms.html, accessed Oct 22nd, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0042","article-title":"High-Precision computation and mathematical physics","author":"Bailey","year":"2008","journal-title":"Proc. Sci.: XII Adv. Comput. Anal. Tech. Phys. Res."},{"key":"10.1016\/j.cam.2026.117915_bib0043","unstructured":"Wolfram Research, PolyLog, 2022, (Mathematica), https:\/\/reference.wolfram.com\/language\/ref\/PolyLog.html."},{"key":"10.1016\/j.cam.2026.117915_bib0044","unstructured":"M. Kuhnert, Enhanced Computation of Polylogarithm aka de Jonquieres function, 2026, (Matlab package). https:\/\/www.mathworks.com\/matlabcentral\/fileexchange\/37229-enhanced-computation-of-polylogarithm-aka-de-jonquieres-function, accessed April 9th, 2026."},{"key":"10.1016\/j.cam.2026.117915_bib0045","unstructured":"Mathworks, polylog, 2025, (MAtlab), https:\/\/au.mathworks.com\/help\/symbolic\/sym.polylog.html."},{"key":"10.1016\/j.cam.2026.117915_bib0046","unstructured":"M. Eberl, The Polylogarithm Function, 2025, (technical report). https:\/\/www.isa-afp.org\/browser_info\/current\/AFP\/Polylog\/document.pdf, accessed, 22nd Oct., 2025."},{"issue":"2","key":"10.1016\/j.cam.2026.117915_bib0047","doi-asserted-by":"crossref","first-page":"214","DOI":"10.1016\/0022-314X(85)90052-6","article-title":"The polylogarithm in algebraic number fields","volume":"21","author":"Abouzahra","year":"1985","journal-title":"J. Number Theory"},{"key":"10.1016\/j.cam.2026.117915_bib0048","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1017\/S0027763000001379","article-title":"On polylogarithms","volume":"114","author":"Dupont","year":"1989","journal-title":"Nagoya Math. J."},{"key":"10.1016\/j.cam.2026.117915_bib0049","series-title":"Proceedings of the International Congrress of Mathematicians","article-title":"Polylogarithms in arithmetic and geometry","author":"Goncharov","year":"1994"},{"key":"10.1016\/j.cam.2026.117915_bib0050","unstructured":"D.H. Bailey, D.J. Broadhurst, A seventeenth-order polylogarithm ladder, 1999. arXiv:math\/9906134 [math.CA]."},{"key":"10.1016\/j.cam.2026.117915_bib0051","unstructured":"D. Broadhurst, Dickman polylogarithms and their constants, 2010. arXiv: 1004.0519 [math-ph]."},{"key":"10.1016\/j.cam.2026.117915_bib0052","series-title":"On the Rapid Computation of Various Polylogarithmic Constants","first-page":"663","author":"Bailey","year":"2004"},{"key":"10.1016\/j.cam.2026.117915_bib0053","unstructured":"G.B. Campbell, Polylogarithm approaches to Riemann Zeta function zeroes, 2012.. arXiv: 1212.2246 [math.NT]."},{"key":"10.1016\/j.cam.2026.117915_bib0054","unstructured":"E.W. Weisstein, Hurwitz Zeta Function, 2025, (Mathworld\u2013A Wolfram Resource). https:\/\/mathworld.wolfram.com\/HurwitzZetaFunction.html, access on Oct 22nd, 2025."},{"key":"10.1016\/j.cam.2026.117915_bib0055","doi-asserted-by":"crossref","first-page":"19","DOI":"10.1038\/218019a0","article-title":"Memo functions and machine learning","volume":"218","author":"Michie","year":"1968","journal-title":"Nature"},{"key":"10.1016\/j.cam.2026.117915_bib0056","unstructured":"A. Voigt, Comparison of methods for the calculation of the real dilogarithm regarding instruction-level parallelism, 2022. arXiv: 2201.01678 [hep-ph]."},{"key":"10.1016\/j.cam.2026.117915_bib0057","unstructured":"A. Voigt, An algorithm to approximate the real trilogarithm for a real argument, 2023. arXiv: 2308.11619 [cs.MS]."},{"issue":"5","key":"10.1016\/j.cam.2026.117915_bib0058","doi-asserted-by":"crossref","first-page":"1232","DOI":"10.1137\/0517086","article-title":"Nielsen\u2019s generalized polylogarithms","volume":"17","author":"K\u00f6lbig","year":"1986","journal-title":"SIAM J. Math. Anal."},{"issue":"05","key":"10.1016\/j.cam.2026.117915_bib0059","doi-asserted-by":"crossref","first-page":"725","DOI":"10.1142\/S0217751X00000367","article-title":"Harmonic polylogarithms","volume":"15","author":"Remiddi","year":"2000","journal-title":"Int. J. Mod. Phys. A"},{"key":"10.1016\/j.cam.2026.117915_bib0060","first-page":"1","article-title":"Multiple polylogarithms: an introduction","author":"Waldschmidt","year":"2002","journal-title":"Number Theory and Discrete Mathematics, Trends in Mathematics."}],"container-title":["Journal of Computational and Applied Mathematics"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005571?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S0377042726005571?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,7,10]],"date-time":"2026-07-10T06:49:05Z","timestamp":1783666145000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S0377042726005571"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2027,1]]},"references-count":60,"alternative-id":["S0377042726005571"],"URL":"https:\/\/doi.org\/10.1016\/j.cam.2026.117915","relation":{},"ISSN":["0377-0427"],"issn-type":[{"value":"0377-0427","type":"print"}],"subject":[],"published":{"date-parts":[[2027,1]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"Finite precision computation of the polylogarithm function for complex parameters and arguments","name":"articletitle","label":"Article Title"},{"value":"Journal of Computational and Applied Mathematics","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.cam.2026.117915","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 The Author. Published by Elsevier B.V.","name":"copyright","label":"Copyright"}],"article-number":"117915"}}