On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments

• 作者: Anis Riahi Habib Rebei
• 来源期刊: 应用数学与应用物理(英文)
• 学科: 数学
• 关键词: Three-Term RECURRENCE Relation Quantum Decomposition of Random VARIABLES WITHOUT MOMENTS Lévy-Khintchine Function
• 年，卷（期）: 2018,（3）
• 页码范围: 588-601
• 页数: 14页
• 分类号: O1

摘要

In this paper, we extend the three-term recurrence relation for orthogonal polynomials associated with a probability distribution having a finite moment of all orders to a class of orthogonal functions associated with an infinitely divisible probability distribution µ?having a finite moments of order less or equal to four. An explicit expression of these functions will be given in term of the Lévy-Khintchine function of the measure?µ.