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On the remainder term of Gauss–Radau quadratures for analytic functions

✍ Scribed by Gradimir V. Milovanović; Miodrag M. Spalević; Miroslav S. Pranić

Publisher
Elsevier Science
Year
2008
Tongue
English
Weight
166 KB
Volume
218
Category
Article
ISSN
0377-0427

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✦ Synopsis

For analytic functions the remainder term of Gauss-Radau quadrature formulae can be represented as a contour integral with a complex kernel. We study the kernel on elliptic contours with foci at the points ±1 and a sum of semi-axes > 1 for the Chebyshev weight function of the second kind. Starting from explicit expressions of the corresponding kernels the location of their maximum modulus on ellipses is determined. The corresponding Gautschi's conjecture from [On the remainder term for analytic functions of Gauss-Lobatto and Gauss-Radau quadratures, Rocky Mountain J. Math.

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