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Mathematics of Computation

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

 

 

Computation of the regular continued fraction for Euler's constant


Author: Richard P. Brent
Journal: Math. Comp. 31 (1977), 771-777
MSC: Primary 65D20; Secondary 10-04
DOI: https://doi.org/10.1090/S0025-5718-1977-0436547-7
MathSciNet review: 0436547
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Abstract: We describe a computation of the first 20,000 partial quotients in the regular continued fractions for Euler's constant $ \gamma = 0.577 \ldots $ and $ \exp (\gamma ) = 1.781 \ldots .$ A preliminary step was the calculation of $ \gamma $ and $ \exp (\gamma )$ to 20,700D. It follows from the continued fractions that, if $ \gamma $ or $ \exp (\gamma )$ is of the form $ P/Q$ for integers P and Q, then $ \vert Q\vert > {10^{10000}}$.


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Additional Information

DOI: https://doi.org/10.1090/S0025-5718-1977-0436547-7
Keywords: Euler's constant, Mascheroni's constant, gamma, rational approximation, regular continued fractions, multiple-precision arithmetic, arithmetic-geometric mean, Khintchine's law, Lévy's law, Gauss-Kusmin law
Article copyright: © Copyright 1977 American Mathematical Society