analytic in a neighborhood of infinity will be approximated by Pade approximants. In a first group of results rather strong assumptions are made about the singularities of the function f to be approximated (Assumption 1.1). In a second group (Definition 1.3 and Theorem 1.7) a different type of assum
The convergence and continuity of rational functions closely related to Padé approximants
✍ Scribed by Leslie V Foster
- Publisher
- Elsevier Science
- Year
- 1980
- Tongue
- English
- Weight
- 573 KB
- Volume
- 28
- Category
- Article
- ISSN
- 0021-9045
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📜 SIMILAR VOLUMES
Let \(\psi\) be a finite positive measure on \(\mathbf{R}\), and let \(F_{\psi}(z)=\int_{-x}^{x}(d \psi(t) /(z-t))\) be its Stieltjes transform. A special multipoint Padé approximation problem for \(F_{\psi}(z)\) is studied, where the interpolation points are a finite number of points \(a_{1}, \ldot
We investigate the polynomials P n , Q m , and R s , having degrees n, m, and s, respectively, with P n monic, that solve the approximation problem We give a connection between the coefficients of each of the polynomials P n , Q m , and R s and certain hypergeometric functions, which leads to a sim