Explicit Nearly Optimal Linear Rational Approximation with Preassigned Poles

This paper gives explicit rational functions for interpolating and approximating functions on the intervals [-1,1], [0, oo], and [-oo, oo]. The rational functions are linear in the functions to be approximated, and they have preassigned poles. The error of approximation of these rationals is nearly as small as the error of best rational approximation with numerator and denominator polynomials of the same degrees. Regions of analyticity are described, which make it possible to tell a priori the accuracy which we can expect from this type of rational approximation.