A Lower Bound for Rational Approximations to π Original Research Article

We give a sharp lower bound for rational approximations to π by modifying the classical approximation formula to the system {(log(1 − x))j}1 ≤ j ≤ K due to Hermite. In fact, it will he shown that π has an irrationality measure (less than) 13.398, which improves the earlier result announced by D. V. Chudnovsky and G. V. Chudnosvsky.