5 papers
Where did the examples of Abel's continuity theorem go?
Sergio A. Carrillo
Abel's continuity theorem for power series is a great tool to compute sums and prove properties of special functions. However, apart from two basic examples, this no longer occupie…
Appell and Sheffer sequences: on their characterizations through functionals and examples
Sergio A. Carrillo, Miguel Hurtado
The aim of this paper is to present a new simple recurrence for Appell and Sheffer sequences in terms of the linear functional that defines them, and to explain how this is equival…
Bernoulli and Euler numbers from divergent series
Sergio A. Carrillo
The aim of this note is to provide a simple proof of some well-known identities and recurrences relating classical Bernoulli and Euler numbers by using the Abel sum of the divergen…
Tauberian theorems for --summability with respect to an analytic germ
Sergio A. Carrillo, Jorge Mozo-Fernández, Reinhard Schäfke
The goal of this article is to establish tauberian theorems for the --summability processes defined by germs of analytic functions in several complex variables. The proofs are b…
Summability in a monomial for some classes of singularly perturbed partial differential equation
Sergio A. Carrillo
The aim of this paper is to continue the study of asymptotic expansions and summability in a monomial in any number of variables. In particular we characterize these expansions in…