On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments - Journal of Applied Mathematics and Physics

JAMP > Vol.6 No.3, March 2018

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

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Download as PDF (Size: 331KB) PP. 588-601

DOI: 10.4236/jamp.2018.63051 520 Downloads 1,462 Views

Author(s)

Habib Rebei, Anis Riahi

Affiliation(s)

Department of Mathematics, College of Science, Qassim University, Al-Mulida, Saudi Arabia.

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 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.

KEYWORDS

Three-Term Recurrence Relation, Quantum Decomposition of Random Variables Without Moments, Lévy-Khintchine Function

Share and Cite:

Rebei, H. and Riahi, A. (2018) On the Extension of the Three-Term Recurrence Relation to Probabilities Distributions without Moments. Journal of Applied Mathematics and Physics, 6, 588-601. doi: 10.4236/jamp.2018.63051.

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