Euler's constant to places

Author:
Donald E. Knuth

Journal:
Math. Comp. **16** (1962), 275-281

MSC:
Primary 10.41

DOI:
https://doi.org/10.1090/S0025-5718-1962-0148255-X

MathSciNet review:
0148255

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Abstract | References | Similar Articles | Additional Information

Abstract: The value of Euler's or Mascheroni's constant

**[1]**L. Euler, ``De progressionibus harmonicis observationes,''*Euleri Opera Omnia Ser. 1*, v. 14, Teubner, Leipzig and Berlin, 1925, p. 93-100.**[2]**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.**[3]**J. W. L. Glaisher, ``On the calculation of Euler's constant,''*Proc. Roy. Soc. London*, v. 19, 1870, p. 514-524.**[4]**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.**[5]**J. W. L. Glaisher, ``History of Euler's constant,''*Messenger of Mathematics*, v. 1, 1872, p. 25-30.**[6]**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.**[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****[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**, https://doi.org/10.1145/367487.367499**[11]**Daniel Shanks and John W. Wrench Jr.,*Calculation of 𝜋 to 100,000 decimals*, Math. Comp.**16**(1962), 76–99. MR**0136051**, https://doi.org/10.1090/S0025-5718-1962-0136051-9**[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**, https://doi.org/10.1090/S0025-5718-1960-0170455-1**[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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DOI:
https://doi.org/10.1090/S0025-5718-1962-0148255-X

Article copyright:
© Copyright 1962
American Mathematical Society