系数为±1的符号幂级数的任意阶Padé逼近的存在性和收敛性

ON THE EXISTENCE AND CONVERGENCE OF FORMAL POWER SERIES WITH SION COEFFICIENTS

本文讨论了形如 f(z)=ε_0+ε_1z+ε_z^2+…的幂级数的任意阶Pade逼近的存在性和收敛性问题,这里ε_n=±1,(n=0,1,…)。给出了任意行Pade逼近的一个一致收敛区域。

In this paper, the author investigates the existence and the convergence of Pade approximants of the formal power series f(z)=ε_0+ε_1z+ε_2z^2+… where ε_n=±1, (n=0, 1, 2, …)。A uniform Convergence region of any row Pade approximants is given.