Probabilistic approach to Appell polynomials
Copyright policy )Probabilistic approach to Appell polynomials
In this paper we study Appell polynomials by connecting them to random variables. This probabilistic approach yields, e.g., the mean value property which is fundamental in the sense that many other properties can be derived from it. We also discuss moment representations of Appell polynomials. In the latter part of the paper the presented general theory is applied to study some classical explicitly given polynomials.
- Åbo Akademi University Finland
gamma distribution, 11B68, 33C45, 60E05, Bernoulli, Probability (math.PR), Appell polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Euler, FOS: Mathematics, Probability distributions: general theory, Laguerre polynomials, Bernoulli and Euler numbers and polynomials, Hermite, Mathematics - Probability
gamma distribution, 11B68, 33C45, 60E05, Bernoulli, Probability (math.PR), Appell polynomials, Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.), Euler, FOS: Mathematics, Probability distributions: general theory, Laguerre polynomials, Bernoulli and Euler numbers and polynomials, Hermite, Mathematics - Probability
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).25 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Top 10% influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!