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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 \(|z|\leq 1/2\), the Gaussian quadrature is used with a relative error of \(1.8\times 10^{-18}\) at most.

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

Software:

Mathematica
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Full Text: DOI

References:

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