  The main goal in this manuscript is to 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.
Quadrature rules and other properties based on the zeros of these functions are
also considered.
