On the Computation of Euler’s Constant

  • Dura W. Sweeney


The computation of Eider’s constant, γ, to 3566 decimal places by a procedure not previously used is described. As a part of this computation, the natural logarithm of 2 has been evaluated to 3683 decimal places. A different procedure was used in computations of γ performed by J. C. Adams in 1878 [1] and J. W. Wrench, Jr. in 1952 [2], and recently by D. E. Knuth [3]. This latter procedure is critically compared with that used in the present calculation. The new approximations to γ and ln 2 are reproduced in extenso at the end of this paper.


Decimal Place Individual Term Bernoulli Number Multiplication Loop Intermediate Computation 
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  1. 1.
    J. C. Adams, “On the value of Euler’s constant,” Proc. Roy. Soc. London, v. 27, 1878, p. S8–94.Google Scholar
  2. 2.
    J. W. Wrench, Jr., “A new calculation of Euler’s constant,” MTAC, v. 6, 1952, p. 255.Google Scholar
  3. 3.
    D. E. Knuth, “Euler’s constant to 1271 places,” Math. Comp., v. 16, 1962, p. 275–281.MATHMathSciNetGoogle Scholar
  4. 4.
    H. S. Uhler, “Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7, and 17,” Proc. Nat. Acad. Sei., v.26, 1940, p. 205–212.CrossRefMATHMathSciNetGoogle Scholar

Copyright information

© Springer Science+Business Media New York 2004

Authors and Affiliations

  • Dura W. Sweeney
    • 1
  1. 1.IBM Data Processing DivisionPoughkeepsieUSA

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