TITLE:
On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments
AUTHORS:
Habib Rebei, Anis Riahi
KEYWORDS:
Three-Term Recurrence Relation, Quantum Decomposition of Random Variables Without Moments, Lévy-Khintchine Function
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.6 No.3,
March
28,
2018
ABSTRACT: 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 µhaving 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 measureµ.