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

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Document pages: 14 pages

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

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