当前位置: X-MOL 学术Comput. Methods Funct. Theory › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
On Overconvergence of Closed to Row Subsequences of Classical Padé Approximants
Computational Methods and Function Theory ( IF 2.1 ) Pub Date : 2020-01-29 , DOI: 10.1007/s40315-020-00301-4
Ralitza Kovacheva

Let \(f(z) := \sum f_\nu z^\nu \) be a power series with positive radius of convergence. In the present paper, we study the phenomenon of overconvergence of sequences of classical Padé approximants \(\{\pi _{n,m_n}\}\) associated with f, where \(m_n\rightarrow \infty \), \(m_n\le m_{ n+1}\le m_n+1\) and \(m_n = o(n/\log n)\), resp. \(m_n = o(n)\) as \(n\rightarrow \infty \). We extend classical results by J. Hadamard and A. A. Ostrowski related to overconvergent Taylor polynomials, as well as results by G. López Lagomasino and A. Fernándes Infante concerning overconvergent subsequences of a fixed row of the Padé table.

中文翻译:

关于经典Padé逼近的封闭行列的超收敛性

\(f(z):= \ sum f_ \ nu z ^ \ nu \)是具有正收敛半径的幂级数。在本文中,我们研究了与f关联的经典Padé近似值\(\ {\ pi _ {n,m_n} \} \)的序列的过度收敛现象,其中\(m_n \ rightarrow \ infty \)\( m_n \ le m_ {n + 1} \ le m_n + 1 \)\(m_n = o(n / \ log n)\)\(m_n = o(n)\)\(n \ rightarrow \ infty \)。我们扩展了J. Hadamard和AA Ostrowski关于超收敛泰勒多项式的经典结果,以及G.LópezLagomasino和A.FernándesInfante关于Padé表固定行的超收敛子序列的结果。
更新日期:2020-01-29
down
wechat
bug