Error estimation of Gaussian quadrature formulae for some modifications of Jacobi weights in the class of analytic functions

Abstract

For analytic functions in a neighborhood of the real interval $[-1,1]$, we study the remainder terms
of Gauss quadrature rules with respect to some modifications of Jacobi
weight functions, namely
\[
\omega_1(x)=\dfrac{(1-x)^{\alpha}(1+x)^{\beta}}{v-x}\,\quad \omega_2(x)=\left(v-x\right)(1-x)^{\alpha}(1+x)^{\beta} 
\]
where $\alpha, \beta>-1$ and $v\in\mathbb{R}, |v|>1$. Quadrature formulas concerned with this kind of weight functions have been considered recently by D.~Lj Djuki\'c et al.