A class of orthogonal functions given by a three term recurrence formula

Bracciali, C.; McCabe, J.; Pérez, T.; Ranga, A.

doi:10.1090/mcom3041

A class of orthogonal functions given by a three term recurrence formula
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by C. F. Bracciali, J. H. McCabe, T. E. Pérez and A. Sri Ranga PDF

Math. Comp. 85 (2016), 1837-1859 Request permission

Abstract:

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.

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