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Convolution identities for scale transformations of Appell polynomials
José A. Adell, Alberto Lekuona
We obtain closed form expressions for convolutions of scale transformations within a certain subset of Appell polynomials. This subset contains the Bernoulli, Apostol-Euler, and Ca…
Explicit expressions for higher order convolutions of Cauchy numbers
José A. Adell, Alberto Lekuona
We give explicit expressions for higher order convolutions of Cauchy numbers, either as one single integral or in terms of the Stirling numbers of the first and second kinds.
Closed form expressions for Appell polynomials
José A. Adell, Alberto Lekuona
We show that any Appell sequence can be written in closed form as a forward difference transformation of the identity. Such transformations are actually multipliers in the abelian…
A probabilistic generalization of the Stirling numbers of the second kind
José A. Adell, Alberto Lekuona
Associated to each random variable having a finite moment generating function, we introduce a different generalization of the Stirling numbers of the second kind. Some characte…