Osácar, Carlos; Palacián, Jesús; Palacios, Manuel Numerical evaluation of the dilogarithm of complex argument. (English) Zbl 0830.65013 Celest. Mech. Dyn. Astron. 62, No. 1, 93-98 (1995). An algorithm for evaluating the dilogarithmic function of a complex argument is proposed. In this proposal, three approximations are provided according to the different regions of the complex plane. For the arguments \(|z|\leq 1/2\), the Gaussian quadrature is used with a relative error of \(1.8\times 10^{-18}\) at most. Reviewer: Y.Kobayashi (Tottori) Cited in 5 Documents MSC: 65D20 Computation of special functions and constants, construction of tables 65E05 General theory of numerical methods in complex analysis (potential theory, etc.) 70F15 Celestial mechanics 30E10 Approximation in the complex plane Keywords:convergence acceleration; algorithm; dilogarithmic function; Gaussian quadrature Software:Mathematica PDFBibTeX XMLCite \textit{C. Osácar} et al., Celest. Mech. Dyn. Astron. 62, No. 1, 93--98 (1995; Zbl 0830.65013) Full Text: DOI Digital Library of Mathematical Functions: §25.18(i) Function Values and Derivatives ‣ §25.18 Methods of Computation ‣ Computation ‣ Chapter 25 Zeta and Related Functions References: [1] Abramowitz, M. and Stegun, I. A.: 1985,Handbook of Mathematical Functions, Dover Publications Inc, New York. · Zbl 0171.38503 [2] Burden, R. L. and Faires, J. D.: 1993,Numerical Analysis, PWS-KENT Publishing Company, Boston. · Zbl 0788.65001 [3] Ginsberg, E. S. and Zaborowski, D.: 1973 The Dilogarithm Function of a Real Argument,Collected Algorithms from CACM 490, 1-0. [4] Lewin, L.: 1958,Dilogarithms and Associated Functions, Macdonald Ed., London. · Zbl 0083.35904 [5] Osácar, C. and Palacián, J.: 1994,Celes. Mech & Dynam. Astron. 60, 207. · Zbl 0822.70008 · doi:10.1007/BF00693322 [6] Rall, K. and Jones, L.: 1992,Language Systems, FORTRAN 3.0, Reference Manual, Language Systems Corporation, Herndon, VA. [7] Van Wijngaarden, A.: 1954,Polylogarithms, by the Staff of the Computation Department, Report R. 24, Part I, Numerical Values, Mathematisch Centrum, Amsterdam, Holland. [8] Wolfram, S.: 1991,Mathematica. A System for Doing Mathematics by Computer, Second edition. Addison-Wesley Publishing Company, Inc., Redwood City, CA. · Zbl 0671.65002 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.