Rational approximation to the exponential function with complex conjugate interpolation points (Q5945608)

The paper begins by a complete historical review of all problems related to rational approximation and interpolation to the exponential function discussing essentially the convergence aspects. Then the author studies the problem of convergence as well as the asymptotic error estimates of rational interpolants in the case of complex interpolation points. The solved problem concerns the particular case where those points are conjugate and lie in horizontal strips of arbitrary length, but with height less then \(4\pi\). The error estimates given in compact sets of \(\mathbb C\) generalize the classical estimates for Padé approximants to the exponential function.