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Open AccessArticle

From Circular to Bessel Functions: A Transition through the Umbral Method

1
ENEA— Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
2
Department of Mathematics, University of Catania, Via Santa Sofia, 64, 95125 Catania, Italy
*
Author to whom correspondence should be addressed.
Fractal Fract 2017, 1(1), 9; https://doi.org/10.3390/fractalfract1010009
Received: 9 October 2017 / Revised: 3 November 2017 / Accepted: 3 November 2017 / Published: 8 November 2017
(This article belongs to the Special Issue Fractional Dynamics)
A common environment in which to place Bessel and circular functions is envisaged. We show, by the use of operational methods, that the Gaussian provides the umbral image of these functions. We emphasize the role of the spherical Bessel functions and a family of associated auxiliary polynomials, as transition elements between these families of functions. The consequences of this point of view and the relevant impact on the study of the properties of special functions is carefully discussed. View Full-Text
Keywords: Bessel functions; Hermite polynomials; umbral calculus Bessel functions; Hermite polynomials; umbral calculus
MDPI and ACS Style

Dattoli, G.; Di Palma, E.; Licciardi, S.; Sabia, E. From Circular to Bessel Functions: A Transition through the Umbral Method. Fractal Fract 2017, 1, 9.

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