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.
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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.
Orthogonal functions, Orthogonal polynomials on the unit circle, Quadrature rules, Self-inversive polynomials, Three term recurrence
Mathematics of Computation, v. 85, n. 300, p. 1837-1859, 2016.