English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

In this paper, we consider the Gauss quadrature formulae corresponding tosome modifications of anyone of the four Chebyshev weights, considered byGautschi and Li in \cite{gauli}. As it is well known, in the case of analyticintegrands, the error of these quadrature formulas can be represented as acontour integral with a complex kernel. We study the kernel, as it is oftenconsidered, on elliptic contours with foci at the points $\mp 1$ and such thatthe sum of semi-axes is $\rho>1$, of the mentioned quadrature formulas, andderive some error bounds for them. In addition, we obtain, for the first timeas far as we know, a result about the behavior of the modulus of thecorresponding kernels on those ellipses in some cases. Numerical exampleschecking the accuracy of such error bounds are included.

The error bounds of Gauss quadrature formulae for the modified weight functions of Chebyshev type