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

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551307-4

MathSciNet review:
551307

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Abstract: We describe several new algorithms for the high-precision computation of Euler's constant Using one of the algorithms, which is based on an identity involving Bessel functions, has been computed to 30,100 decimal places. By computing their regular continued fractions we show that, if or is of the form for integers *P* and *Q*, then .

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Additional Information

DOI:
https://doi.org/10.1090/S0025-5718-1980-0551307-4

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