Rational Gauss-Chebyshev quadrature formulas for complex poles outside $[-1,1

Abstract

In this paper we provide an extension of the Chebyshev orthogonal rational functions with arbitrary real poles outside [-1,1] to arbitrary complex poles outside [-1,1]. The zeros of these orthogonal rational functions are not necessarily real anymore. By using the related para-orthogonal functions, however, we obtain an expression for the nodes and weights for rational Gauss-Chebyshev quadrature formulas integrating exactly in spaces of rational functions with arbitrary complex poles outside [-1,1].