A unified approach to higher order convolutions within a certain subset of appell polynomials

Adell, José A. (Universidad de Zaragoza) ; Lekuona, Alberto (Universidad de Zaragoza)

Resumen: We consider the subset R of Appell polynomials whose exponential generating function is given in terms of the moment generating function of a certain random variable Y. This subset contains the Hermite, Bernoulli, Apostol–Euler, and Cauchy type polynomials, as well as various kinds of their generalizations, among others. We obtain closed form expressions for higher order convolutions of Appell polynomials in the subset R. We give a unified approach mainly based on random scale transformations of Appell polynomials, as well as on a probabilistic generalization of the Stirling numbers of the second kind. Different illustrative examples, including reformulations of convolution identities already known in the literature, are discussed in detail. In such examples, the convolution identities involve the classical Stirling numbers.

Idioma: Inglés

DOI: 10.1007/s00009-020-1480-1

Año: 2020

Publicado en: Mediterranean Journal of Mathematics 17, 2 (2020), 63 [17 pp.]
ISSN: 1660-5446

Factor impacto JCR: 1.4 (2020)

Categ. JCR: MATHEMATICS, APPLIED rank: 129 / 265 = 0.487 (2020) - Q2 - T2
Categ. JCR: MATHEMATICS rank: 88 / 330 = 0.267 (2020) - Q2 - T1

Factor impacto SCIMAGO: 0.695 - Mathematics (miscellaneous) (Q2)

Financiación: info:eu-repo/grantAgreement/ES/DGA/E64
Financiación: info:eu-repo/grantAgreement/ES/MINECO/MTM2015-67006-P

Tipo y forma: Artículo (PostPrint)

Área (Departamento): Área Estadís. Investig. Opera. (Dpto. Métodos Estadísticos)