E2 -computability of e, π and Other Famous Constants

  • Authors:
  • Dimiter Skordev

  • Affiliations:
  • Faculty of Mathematics and Informatics, Sofia University, Sofia, Bulgaria

  • Venue:
  • Electronic Notes in Theoretical Computer Science (ENTCS)
  • Year:
  • 2008

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Abstract

We show that e, @p and other remarkable real numbers are limits of E^2-computable sequences of rational numbers having a polynomial rate of convergence (as usual, E^2 denotes the second Grzegorczyk class). However, only the rational numbers are limits of E^2-computable sequences of rational numbers with an exponential rate of convergence.