由三重递推公式给出的一类正交函数
A class of orthogonal functions given by a three term recurrence formula
Universidade Estadual Paulista（圣保罗州立大学）；University of St.Andrews（圣安德鲁斯大学）；Universidad de Granada（格拉纳达大学）
AI总结：
本文研究一类满足正交性质且具有三重递推公式的函数，扩展了对称正交多项式，并探讨其与单位圆上正交多项式的关系及相关数值方法。
摘要：
本文的主要目标是介绍一类满足特定正交性质且存在三重递推公式的函数。这类函数可视为对称正交多项式在[-1,1]上的扩展，与单位圆上的正交多项式有完整联系。还考虑了基于这些函数零点的求积公式及其他性质。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
