代数S-围线上带解析权的Nuttall定理
Nuttall's theorem with analytic weights on algebraic S-contours
摘要：
给定一个在无穷远处全纯的函数$f$，$f$的$n$次对角Padé逼近，记为$[n/n]_f$，是一个$(n,n)$型有理函数，它在无穷远处与$f$有最高阶的接触。Nuttall定理给出了当$f$是光滑密度关于[-1，1]上反正弦分布的柯西积分时，逼近误差$f-[n/n]_f$的渐近公式.本文将Nuttall定理推广到代数S-围线上解析密度的Cauchy积分（在Nuttall和Stahl意义下）。
英文摘要：
Given a function $f$ holomorphic at infinity, the $n$-th diagonal Padé approximant to $f$, denoted by $[n/n]_f$, is a rational function of type $(n,n)$ that has the highest order of contact with $f$ at infinity. Nuttall's theorem provides an asymptotic formula for the error of approximation $f-[n/n]_f$ in the case where $f$ is the Cauchy integral of a smooth density with respect to the arcsine distribution on [-1,1]. In this note, Nuttall's theorem is extended to Cauchy integrals of analytic densities on the so-called algebraic S-contours (in the sense of Nuttall and Stahl).
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