E2 -computability of e, π and Other Famous Constants
Dimiter G. Skordev · Electronic Notes in Theoretical Computer Science · 2008
We show that e, π and other remarkable real numbers are limits of E2-computable sequences of rational numbers having a polynomial rate of convergence (as usual, E2 denotes the second Grzegorczyk class). However, only the rational numbers are limits of E2-computable sequences of rational numbers with an exponential rate of convergence.