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On certain symmetric strong distributions, two-point Padé approximation and related quadratures. (English) Zbl 1166.30018

Summary: Let \(\phi\) be a \(c\)-inversive strong distribution as defined in [ A. Sri Ranga, E.X.L. de Andrade, J.H. McCabe, J. Math. Anal. Appl. 193 (1), 158–168 (1995; Zbl 0831.41016)]. In this paper, two-point Padé approximants, both with free and prescribed poles, related to the distribution \(\phi\) are analyzed. In particular, the existence of \(c\)-inversive rational approximants to the Stieltjes transform of \(\phi\) is studied, in order to make computations in an advantageous way. An application to numerical quadratures is also given, and several examples applying these Gauss-type quadrature formulas in the case of integrands which can be well approximated by Laurent polynomials are displayed, showing better results than the corresponding for the usual Gaussian rules.

MSC:

30E10 Approximation in the complex plane
41A21 Padé approximation
34E05 Asymptotic expansions of solutions to ordinary differential equations

Citations:

Zbl 0831.41016

Software:

ARPREC
PDFBibTeX XMLCite
Full Text: DOI

References:

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