Rational approximation on infinite intervals

We describe some approximation properties of polynomials of degree at most 2n withweight (1 + χ2)−n on the real line and of polynomials of degree at most n with weight (1 + t)−n on the interval [0, ∞). This article is intended to summarize the results of a systematic investigation; most of the results have very recently appeared elsewhere, or will soon appear.