Gaussian rational quadrature formulas for ill-scaled integrands

A flexible treatment of Gaussian quadrature formulas based on rational functions is given to evaluate the integral ∫ I f ( x ) W ( x ) d x , when f is meromorphic in a neighborhood V of the interval I and W ( x ) is an ill-scaled weight function. Some numerical tests illustrate the power of this approach in comparison with Gautschi’s method.