The asymptotic accuracy of rational best approximations to \(e^ z\) on a disk
D. Braess has recently proved the Meinardus conjecture regarding degree of approximation of \(e^ z\) on the unit interval by rational functions of type (m,n). The present paper uses Braess's method to prove an analogous result for approximation of \(e^ z\) on the unit disk: as \(m+n\) approaches \(\infty\), the best approximation error has the behavior \(E_{mn}\sim m!n!/(m+n)!(m+n+1)!.\)
scientific article; zbMATH DE number 3867912