Result: a α acceptability of rational approximations to function exp z: \(A(\alpha)\)-acceptability of rational approximations to function \(\exp(z)\)

Title:
a α acceptability of rational approximations to function exp z: \(A(\alpha)\)-acceptability of rational approximations to function \(\exp(z)\)
Authors:
Yang Fengjian, Chen Xinming
Source:
Approximation Theory and Its Applications. 17(3):54-59
Publisher Information:
Nanjing University, Nanjing; Kluwer Academic Publishers, Dordrecht, 2001.
Publication Year:
2001
Subject Terms:
exponential, Approximation by rational functions, \(A(\alpha)\)-acceptability, rational approximation, \(A\)-acceptability
Document Type:
Academic journal Article
File Description:
application/xml
ISSN:
1000-9221
DOI:
10.1023/a:1015598111682
Access URL:
https://link.springer.com/content/pdf/10.1023/A:1015598111682.pdf
https://link.springer.com/article/10.1023/A%3A1015598111682
Accession Number:
edsair.dedup.wf.002..3dcb7d54f95522c93f110bb66f30ce9e
Database:
OpenAIRE

Further Information

Two necessary and sufficient conditions, and a sufficient condition of \(A(\alpha)\)-acceptability for \((n,m)\) rational approximation to the function \(\exp(t)\) are given for \(\alpha\in (0,{\pi\over 2})\). Moreover, a necessary and sufficient condition of \(A\)-acceptability for \((n,m)\) rational approximation to \(\exp(z)\) of order \(p\) is obtained, where \(n\leq m\leq p\).