A-acceptability of derivatives of rational approximations to EXP(Z) (Q1070140)

The question of A-acceptability in regard to derivatives of \(R_{m/n}\), the \([m/n]\) Padé approximation to the exponential, is examined for a range of values of \(m\) and \(n\). It is proven that \(R'_{n-1/n}\), \(R'_{n/n}\), \(R'_{n+1/n}\) and \(R''_{n/n}\) are A-acceptable and that numerous other choices of m and n lead to non-A-acceptability. The results seem to indicate that the A-acceptability pattern of \(R^{(k)}_{m/n}\) displays an intriguing generalization of the Wanner-Hairer-Nørsett theorem on the A-acceptability of \(R_{m/n}\).