Some New Algorithms for High-Precision Computation of Euler’s Constant

  • Richard P. Brent
  • Edwin M. McMillan

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

Keywords

Asymptotic Expansion Continue Fraction Partial Quotient Precision Number Involve Bessel Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer Science+Business Media New York 2000

Authors and Affiliations

  • Richard P. Brent
    • 1
    • 2
  • Edwin M. McMillan
    • 1
    • 2
  1. 1.Department of Computer ScienceAustralian National UniversityCanberraAustralia
  2. 2.Lawrence Berkeley LaboratoryUniversity of CaliforniaBerkeleyUSA

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