A class of orthogonal functions given by a three term recurrence formula - Bracciali, C. F. [UNESP]; McCabe, J. H.; Pérez, T. E.; Sri Ranga, A. (American Mathematical Society (AMS), 2016)
We present a class of functions satisfying a certain orthogonality property for which there also exists a three term recurrence formula. This class of functions, which can be considered as an extension to the class of symmetric orthogonal polynomials on [-1, 1], has a complete connection to the orthogonal polynomials on the unit circle. Interpolatory properties, quadrature rules and other properties based on the zeros of these functions are also considered.
Keywords: Orthogonal functions; Orthogonal polynomials on the unit circle; Quadrature rules; Self-inversive polynomials; Three term recurrence