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

  • Richard P. Brent
  • Edwin M. McMillan


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


Asymptotic Expansion Continue Fraction Partial Quotient Precision Number Involve Bessel Function 
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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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