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Mathematics of Computation

Published by the American Mathematical Society since 1960 (published as Mathematical Tables and other Aids to Computation 1943-1959), Mathematics of Computation is devoted to research articles of the highest quality in computational mathematics.

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

The 2020 MCQ for Mathematics of Computation is 1.78.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.


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
  • J. W. Wrench, Jr., “A new calculation of Euler’s constant,” MTAC, v. 6, 1952, p. 255.
  • David A. Pope and Marvin L. Stein, Multiple precision arithmetic, Comm. ACM 3 (1960), 652–654. MR 0116490, DOI 10.1145/367487.367499
  • Daniel Shanks and John W. Wrench Jr., Calculation of $\pi$ to 100,000 decimals, Math. Comp. 16 (1962), 76–99. MR 136051, DOI 10.1090/S0025-5718-1962-0136051-9
  • D. J. Wheeler, The Calculation of 60,000 Digits of e by the Illiac, Digital Computer Laboratory Internal Report No. 43, University of Illinois, Urbana, 1953.
  • John W. Wrench Jr., Further evaluation of Khintchine’s constant, Math. Comp. 14 (1960), 370–371. MR 170455, DOI 10.1090/S0025-5718-1960-0170455-1
  • R. S. Lehman, A Study of Regular Continued Fractions, Ballistic Research Lab. Report 1066, Aberdeen Proving Ground, Maryland, February 1959.
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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