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Mathematics of Computation
Mathematics of Computation
ISSN 1088-6842(online) ISSN 0025-5718(print)

 

Some new algorithms for high-precision computation of Euler's constant


Authors: Richard P. Brent and Edwin M. McMillan
Journal: Math. Comp. 34 (1980), 305-312
MSC: Primary 10-04; Secondary 10A40, 68C05
MathSciNet review: 551307
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Abstract: We describe several new algorithms for the high-precision computation of Euler's constant $ \gamma = 0.577 \ldots $ Using one of the algorithms, which is based on an identity involving Bessel functions, $ \gamma $ has been computed to 30,100 decimal places. By computing their regular continued fractions we show that, if $ \gamma $ or $ \exp (\gamma )$ is of the form $ P/Q$ for integers P and Q, then $ \vert Q\vert > {10^{15000}}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0025-5718-1980-0551307-4
PII: S 0025-5718(1980)0551307-4
Keywords: Euler's constant, Mascheroni's constant, gamma, Bessel functions, rational approximation, regular continued fractions, multiple-precision arithmetic, Gauss-Kusmin law
Article copyright: © Copyright 1980 American Mathematical Society