Journal of the
Korean Mathematical Society JKMS

In this paper we present the $L^2$-estimation for the kernel $K_n$ of the remaider term for the Gaussian quadrature with respect to one of four Chebyshev weight functions and the error bound of the type on the contour $$ |R_n(f)|\leq \frac{\sqrt{l(\Gamma)}}{2\pi}\max_{z\in\Gamma}|f(z)| \left(\int_{\Gamma}|K_n(z)|^2|dz|\right)^{\frac12}, $$ where $l(\Gamma)$ denotes the length of the contour $\Gamma$.

Keywords: Gaussian quadrature, Chebyshev polynomial

MSC numbers: Primary 65D32