Abstract
We describe several new algorithms for the high-precision computation of Euler’s constant γ = 0.577.... Using one of the algorithms, which is based on an identity involving Bessel functions, γ has been computed to 30,100 decimal places. By computing their regular continued fractions we show that, if γ or exp(γ) is of the form P/Q for integers P and Q, then |Q| >1015000
The work of the first author was supported in part by National Science Foundation grant 1–442427–21164–2 at the University of California, Berkeley. This work was also supported by the U. S. Department of Energy under Contract W-7405-ENG-48.
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Brent, R.P., McMillan, E.M. (2000). Some New Algorithms for High-Precision Computation of Euler’s Constant. In: Pi: A Source Book. Springer, New York, NY. https://doi.org/10.1007/978-1-4757-3240-5_50
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DOI: https://doi.org/10.1007/978-1-4757-3240-5_50
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