Padé approximation of the type \(1/S_ n\) for \(1/f\) on the semi-axis, where \(f(x)\) is from the class \(H^ +(\rho,\omega,\tau)\) (Q677796)
From MaRDI portal
 | This is the item page for this Wikibase entity, intended for internal use and editing purposes. Please use this page instead for the normal view: Padé approximation of the type \(1/S_ n\) for \(1/f\) on the semi-axis, where \(f(x)\) is from the class \(H^ +(\rho,\omega,\tau)\) |
scientific article; zbMATH DE number 999742
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Padé approximation of the type \(1/S_ n\) for \(1/f\) on the semi-axis, where \(f(x)\) is from the class \(H^ +(\rho,\omega,\tau)\) |
scientific article; zbMATH DE number 999742 |
Statements
Padé approximation of the type \(1/S_ n\) for \(1/f\) on the semi-axis, where \(f(x)\) is from the class \(H^ +(\rho,\omega,\tau)\) (English)
0 references
4 September 1997
0 references
Let \(f\) be an entire series with nonnegative coefficients representing an entire function of a prescribed regular growth, \(S_n\) a partial sum of \(f\) and \(\sigma_n(1/f)=\sup_{x\geq 0}\left\{{1\over S_n(x)}-{1\over f(x)}\right\}\) (i.e. a sup of \([0,n]\) Padé approximant error of \(1/f\) on the semi-axis \(\mathbb{R}^+\)). The author improves significantly both, the lower and upper estimates for \(\sigma_n\). The English translation contains some mistakes; for instance on the first line ``integer function'', must be replaced by ``entire function''.
0 references
Padé approximation of the entire functions
0 references
Padé approximant error
0 references
