Author

Fei Xue

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Preprint Oct 2026

Convergence of repeated-pole rational approximation of the exponential on infinite sectors

For $h>0$, degree $m\ge0$, $0\le\beta<\pi$, and $q>0$, let $\Sigma_\beta=\{re^{i\theta}:r\ge0,\ |\theta|\le\beta/2\}$ and let $E_{m,\beta}(q)$ denote the best uniform error for approximating $e^{-hz}$ on $\Sigma_\beta$ by rational functions whose only possible finite pole is $s=-q/h$, with multiplicity at most $m$. For...

Fei Xue, Tian-Qi Zhang · 0 citations

Preprint Sep 2026

Uniform Chebyshev asymptotics for repeated-pole rational approximation of the exponential

We study uniform approximation of $\exp(tz)$, $t>0$, on $(-\infty,0]$ by rational functions $P_m(z)/(q_m-z)^m$ with a prescribed repeated pole $q_m>0$. A M\"obius transformation reduces the problem to polynomial approximation of $F_\lambda(x)=\exp\!\left(-\lambda\frac{1-x}{1+x}\right)$ on $[-1,1]$, where $\lambda=tq_m$...

Fei Xue, Tian-Qi Zhang · 1 citation