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

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.