Weighted quadrature rules with binomial nodes

Abstract

In this paper, a new class of a weighted quadrature rule is represented as<br /> -------------------------------------------- <br /> where is a weight function, are interpolation nodes, are the corresponding weight coefficients and denotes the error term. The general form of interpolation nodes are considered as that and we obtain the explicit expressions of the coefficients using the q-binomial theorem. We give an error analysis for the introduced formula and finally we illustrate its application with some numerical examples.