Theory of Hermite and Laguerre Bessel function from the umbral point of view

M. Artioli, G. Dattoli and U. Zainab

Applied Mathematics and Computation, 2025, vol. 488, issue C

Abstract: The theoretical underpinnings of hybrid families of special functions are examined through an umbral reformulation. Our discussion encompasses diverse families of Bessel-type functions and special polynomials, all situated within a unifying umbral-algebraic formalism. The method presented capitalizes on recent advancements in the formal treatment of higher transcendental functions, enabling novel and intriguing generalizations.

Keywords: Hermite polynomials; Laguerre polynomials; Bessel functions; Tricomi functions; Operational rules; Definite integrals (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:488:y:2025:i:c:s0096300324005642

DOI: 10.1016/j.amc.2024.129103

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