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Numerical evaluation of the dilogarithm of complex argument. (English) Zbl 0830.65013
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|1/2, the Gaussian quadrature is used with a relative error of 1·8×10 -18 at most.
MSC:
65D20Computation of special functions, construction of tables
65E05Numerical methods in complex analysis
70F15Celestial mechanics
30E10Approximation in the complex domain
Software:
Mathematica
References:
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[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.
[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.