On Rational Lacunary Approximation on the Interval [−1, 1] Original Research Article

The present paper discusses the approximation by rational combinations of {xnj}∞j=1 on the interval [−1, 1] for a given sequence of nonnegative distinct increasing integers {nj}. We find that the gaps between odd and even numbers or between even and odd numbers of this sequence might be essential in this rational approximation case. This behavior is different from the polynomial approximation case.