Real pole approximations to the exponential function (Q1174453)

It is proved that the best rational approximation to the exponential with real poles in fact has only one multiple pole. It is also known [\textit{S. L. Keelung}, BIT 29, No. 1, 91-109 (1989; Zbl 0673.65050)] that the more general approximants are only \(A\)-acceptable for the same degrees as the special case so nothing is to be gained in that respect either. There is also a further discussion on \(A\)-acceptability of restricted Padé approximants (the multiple pole case) with a couple of conjectures.