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Mathematics of Computation

Published by the American Mathematical Society, the Mathematics of Computation (MCOM) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6842 (online) ISSN 0025-5718 (print)

The 2020 MCQ for Mathematics of Computation is 1.98.

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Euler’s constant to $1271$ places
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by Donald E. Knuth PDF
Math. Comp. 16 (1962), 275-281 Request permission


The value of Euler’s or Mascheroni’s constant \[ \gamma = \underset {n\to \infty }{\lim } (1 + \tfrac {1}{2} + \cdots + ({1}/{n}) - \ln n)\] has now been determined to 1271 decimal places, thus extending the previously known value of 328 places. A calculation of partial quotients and best rational approximations to $\gamma$ was also made.
    L. Euler, “De progressionibus harmonicis observationes,” Euleri Opera Omnia Ser. 1, v. 14, Teubner, Leipzig and Berlin, 1925, p. 93-100. L. Euler, “De summis serierum numeros Bernoullianos involventium,” Euleri Opera Omnia Ser. 1, v. 15, Teubner, Leipzig and Berlin, 1927, p. 91-130. See especially p. 115. The calculation is given in detail on p. 569-583. J. W. L. Glaisher, “On the calculation of Euler’s constant,” Proc. Roy. Soc. London, v. 19, 1870, p. 514-524. W. Shanks, “On the numerical value of Euler’s constant,” Proc. Roy. Soc. London, v. 15, 1867, p. 429-432; v. 20, 1871, p. 29-34. J. W. L. Glaisher, “History of Euler’s constant,” Messenger of Mathematics, v. 1, 1872, p. 25-30. J. C. Adams, “On the value of Euler’s constant,” Proc. Roy. Soc. London, v. 27, 1878, p. 88-94. See also v. 42, 1887, p. 22-25. K. Knopp, Theory and Application of Infinite Series, Blackie and Son, London, 1951, p. 257.
  • J. W. S. Cassels, An introduction to Diophantine approximation, Cambridge Tracts in Mathematics and Mathematical Physics, No. 45, Cambridge University Press, New York, 1957. MR 0087708
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  • David A. Pope and Marvin L. Stein, Multiple precision arithmetic, Comm. ACM 3 (1960), 652–654. MR 0116490, DOI 10.1145/367487.367499
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Additional Information
  • © Copyright 1962 American Mathematical Society
  • Journal: Math. Comp. 16 (1962), 275-281
  • MSC: Primary 10.41
  • DOI:
  • MathSciNet review: 0148255