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The dilogarithm function of a real argument


Author: Robert Morris
Journal: Math. Comp. 33 (1979), 778-787
MSC: Primary 65D20; Secondary 33A70
DOI: https://doi.org/10.1090/S0025-5718-1979-0521291-X
MathSciNet review: 521291
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Abstract: This paper is a user's guide to the dilogarithm function

$\displaystyle L{i_2}(z) = - \int_0^z {\frac{{\log (1 - z)}}{z}} \;dz$

of a real argument. It is intended for those who are primarily interested in the values of the dilogarithm rather than in its functional relationships.

The paper is deliberately written in the style of the book Computer Approximations by Hart, Cheney et al.


References [Enhancements On Off] (What's this?)

  • [1] L. Lewin, Dilogarithms and associated functions, Foreword by J. C. P. Miller, Macdonald, London, 1958. MR 0105524
  • [2] M. ABRAMOWITZ & I. A. STEGUN, Editors, Handbook of Mathematical Functions, with Formulas, Graphs, and Mathematical Tables, Nat. Bur. Standards Appl. Math. Series #55, U.S. Government Printing Office, Washington, D. C., 1964.
  • [3] EDWARD S. GINSBERG & DOROTHY ZABOROWSKY, "Algorithm 490: The dilogarithm function of a real argument," Comm. ACM, v. 18, 1975, pp. 200-202.
  • [4] R. MORRIS, "Remark on Algorithm 490," ACM Trans. Math. Software, v. 2, March 1976, p. 112.
  • [5] JOHN F. HART, E. W. CHENEY, ET AL., Computer Approximations, Wiley, New York, 1968.

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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1979-0521291-X
Article copyright: © Copyright 1979 American Mathematical Society

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