Abstract
The computation of Euler’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 In 2 are reproduced in extenso at the end of this paper.
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References
J. C. ADAMS, “On the value of Euler’s constant,” Proc. Roy. Soc. London., v. 27, 1878, p. 88–94.
J. W. WRENCH,. JR., “A new calculation of Euler’s constant,” MTÀC, v. 6, 1952. p. 255.
D. E. I1NUTH, “Euler’s constant to 1271 places,” Math. Comp., v. 16, 1962, p. 275–281.
H. S. UHLER, “Recalculation and extension of the modulus and of the logarithms of 2, 3, 5, 7, and 17,” Proc. Nat. Acad. Sci., v. 26, 1940, p. 205–212.
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Sweeney, D.W. (2000). On the Computation of Euler’s Constant. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3240-5_39
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DOI: https://doi.org/10.1007/978-1-4757-3240-5_39
Publisher Name: Springer, New York, NY
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