## Quadrature formulas for rational functions

F. Cala Rodriguez, P. Gonzalez-Vera, and M. Jimenez Paiz

### Abstract

Let $\omega$ be an $\mbox{L}_1$-integrable function on $[-1,1]$ and let us denote $$I_{\omega}(f)=\int_{-1}^1 f(x)\omega(x)dx,$$ where $f$ is any bounded integrable function with respect to the weight function $\omega$. We consider rational interpolatory quadrature formulas (RIQFs) where all the poles are preassigned and the interpolation is carried out along a table of points contained in $\bar{\bf C}$. The main purpose of this paper is the study of the convergence of the RIQFs to $I_\omega(f)$.

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