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Operational vs. Umbral Methods and Borel Transform

2019/08/12 by G. Dattoli, Dattoli, Giuseppe, Silvia Licciardi +1
Mathematics · #05A40 #33B10 #33B15 #33C52 #33C65 #33C99 #44A99 #45P05 #47A62 #47B99 #47G10 #97I50 #Advanced Mathematical Identities #Classical Analysis and ODEs (math.CA) #FOS: Mathematics #Mathematical and Theoretical Analysis #Mathematical functions and polynomials

paper · pdf · doi:10.48550/arxiv.1908.04160

openalex publication_date 2019/08/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Differintegral methods, currently exploited in calculus, provide a fairly unexhausted source of tools to be applied to a wide class of problems involving the theory of special functions and not only. The use of integral transforms of Borel type and the associated formalism will be shown to be an effective means, allowing a link between umbral and operational methods. We merge these two points of view to get a new and efficient method to obtain integrals of special functions and the summation of the associated generating functions as well.

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