A Unified Theory for Real vs Complex Rational Chebyshev Approximation on an Interval

A unified approach is presented for determining all the constants $\gamma_{m,n} (m \geq 0, n \geq 0)$ which occur in the study of real vs. complex rational Chebyshev approximation on an interval. In particular, it is shown that $\gamma_{m,m+2} = 1/3 (m \geq 0)$, a problem which had remained open.