Orthogonal polynomials, associated polynomials and functions of the second kind
Journal of Computational and Applied Mathematics - Special volume on the occasion of the 65th birthday of Professor C. C. Grosjean
Characterization of orthogonal polynomials with respect to a functional
Proceedings of the international conference (dedicated to Thomas Jan Stieltjes, Jr.) on Orthogonality, moment problems and continued fractions
Quadrature and orthogonal rational functions
Journal of Computational and Applied Mathematics - Special issue on numerical analysis 2000 Vol. V: quadrature and orthogonal polynomials
Orthogonal rational functions and quadrature on an interval
Journal of Computational and Applied Mathematics - Proceedings of the sixth international symposium on orthogonal polynomials, special functions and their applications
Orthogonal rational functions and quadrature on the real half line
Journal of Complexity
Ratio asymptotics for orthogonal rational functions on an interval
Journal of Approximation Theory
An interpolation algorithm for orthogonal rational functions
Journal of Computational and Applied Mathematics - Special Issue: Proceedings of the 10th international congress on computational and applied mathematics (ICCAM-2002)
Computing orthogonal rational functions with poles near the boundary
Computers & Mathematics with Applications
Algorithm 882: Near-Best Fixed Pole Rational Interpolation with Applications in Spectral Methods
ACM Transactions on Mathematical Software (TOMS)
Orthogonal rational functions and rational modifications of a measure on the unit circle
Journal of Approximation Theory
Computing rational Gauss-Chebyshev quadrature formulas with complex poles: The algorithm
Advances in Engineering Software
Orthogonal rational functions on the real half line with poles in [-∞,0]
Journal of Computational and Applied Mathematics - Special issue: Proceedings of the conference on orthogonal functions and related topics held in honor of Olav Njåstad
Full length article: Baxter's difference systems and orthogonal rational functions
Journal of Approximation Theory
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A special class of orthogonal rational functions (ORFs) is presented in this paper. Starting with a sequence of ORFs and the corresponding rational functions of the second kind, we define a new sequence as a linear combination of the previous ones, the coefficients of this linear combination being self-reciprocal rational functions. We show that, under very general conditions on the self-reciprocal coefficients, this new sequence satisfies orthogonality conditions as well as a recurrence relation. Further, we identify the Caratheodory function of the corresponding orthogonality measure in terms of such self-reciprocal coefficients. The new class under study includes the associated rational functions as a particular case. As a consequence of the previous general analysis, we obtain explicit representations for the associated rational functions of arbitrary order, as well as for the related Caratheodory function. Such representations are used to find new properties of the associated rational functions.