Euler's constant to places
Author:
Donald E. Knuth
Journal:
Math. Comp. 16 (1962), 275281
MSC:
Primary 10.41
MathSciNet review:
0148255
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Abstract: The value of Euler's or Mascheroni's constant 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 was also made.
 [1]
L. Euler, ``De progressionibus harmonicis observationes,'' Euleri Opera Omnia Ser. 1, v. 14, Teubner, Leipzig and Berlin, 1925, p. 93100.
 [2]
L. Euler, ``De summis serierum numeros Bernoullianos involventium,'' Euleri Opera Omnia Ser. 1, v. 15, Teubner, Leipzig and Berlin, 1927, p. 91130. See especially p. 115. The calculation is given in detail on p. 569583.
 [3]
J. W. L. Glaisher, ``On the calculation of Euler's constant,'' Proc. Roy. Soc. London, v. 19, 1870, p. 514524.
 [4]
W. Shanks, ``On the numerical value of Euler's constant,'' Proc. Roy. Soc. London, v. 15, 1867, p. 429432; v. 20, 1871, p. 2934.
 [5]
J. W. L. Glaisher, ``History of Euler's constant,'' Messenger of Mathematics, v. 1, 1872, p. 2530.
 [6]
J. C. Adams, ``On the value of Euler's constant,'' Proc. Roy. Soc. London, v. 27, 1878, p. 8894. See also v. 42, 1887, p. 2225.
 [7]
K. Knopp, Theory and Application of Infinite Series, Blackie and Son, London, 1951, p. 257.
 [8]
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
(19,396h)
 [9]
J. W. Wrench, Jr., ``A new calculation of Euler's constant,'' MTAC, v. 6, 1952, p. 255.
 [10]
David
A. Pope and Marvin
L. Stein, Multiple precision arithmetic, Comm. ACM
3 (1960), 652–654. MR 0116490
(22 #7277)
 [11]
Daniel
Shanks and John
W. Wrench Jr., Calculation of 𝜋 to 100,000
decimals, Math. Comp. 16 (1962), 76–99. MR 0136051
(24 #B2090), http://dx.doi.org/10.1090/S00255718196201360519
 [12]
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.
 [13]
John
W. Wrench Jr., Further evaluation of
Khintchine’s constant, Math. Comp. 14 (1960), 370–371.
MR
0170455 (30 #693), http://dx.doi.org/10.1090/S00255718196001704551
 [14]
R. S. Lehman, A Study of Regular Continued Fractions, Ballistic Research Lab. Report 1066, Aberdeen Proving Ground, Maryland, February 1959.
 [1]
 L. Euler, ``De progressionibus harmonicis observationes,'' Euleri Opera Omnia Ser. 1, v. 14, Teubner, Leipzig and Berlin, 1925, p. 93100.
 [2]
 L. Euler, ``De summis serierum numeros Bernoullianos involventium,'' Euleri Opera Omnia Ser. 1, v. 15, Teubner, Leipzig and Berlin, 1927, p. 91130. See especially p. 115. The calculation is given in detail on p. 569583.
 [3]
 J. W. L. Glaisher, ``On the calculation of Euler's constant,'' Proc. Roy. Soc. London, v. 19, 1870, p. 514524.
 [4]
 W. Shanks, ``On the numerical value of Euler's constant,'' Proc. Roy. Soc. London, v. 15, 1867, p. 429432; v. 20, 1871, p. 2934.
 [5]
 J. W. L. Glaisher, ``History of Euler's constant,'' Messenger of Mathematics, v. 1, 1872, p. 2530.
 [6]
 J. C. Adams, ``On the value of Euler's constant,'' Proc. Roy. Soc. London, v. 27, 1878, p. 8894. See also v. 42, 1887, p. 2225.
 [7]
 K. Knopp, Theory and Application of Infinite Series, Blackie and Son, London, 1951, p. 257.
 [8]
 J. W. S. Cassels, An Introduction to Diophantine Approximation, Cambridge University Press, 1957, p. 111. MR 0087708 (19:396h)
 [9]
 J. W. Wrench, Jr., ``A new calculation of Euler's constant,'' MTAC, v. 6, 1952, p. 255.
 [10]
 D. A. Pope & M. L. Stein, ``Multiple precision arithmetic,'' Comm. ACM, v. 3, 1960, p. 652654. MR 0116490 (22:7277)
 [11]
 D. Shanks & J. W. Wrench, Jr., ``Calculation of to 100,000 decimals,'' Math. Comp., v. 16, 1962, p. 7699. MR 0136051 (24:B2090)
 [12]
 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.
 [13]
 J. W. Wrench, Jr., ``Further evaluation of Khintchine's constant,'' Math. Comp., v. 14, 1960, p. 370371. MR 0170455 (30:693)
 [14]
 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
DOI:
http://dx.doi.org/10.1090/S0025571819620148255X
PII:
S 00255718(1962)0148255X
Article copyright:
© Copyright 1962
American Mathematical Society
