Next Article in Journal
The Fractal Nature of an Approximate Prime Counting Function
Next Article in Special Issue
A Fractional-Order Infectivity and Recovery SIR Model
Previous Article in Journal
Fractional Divergence of Probability Densities
Previous Article in Special Issue
A Fractional Complex Permittivity Model of Media with Dielectric Relaxation
Article Menu

Export Article

Open AccessArticle
Fractal Fract 2017, 1(1), 9;

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

ENEA— Frascati Research Center, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy
Department of Mathematics, University of Catania, Via Santa Sofia, 64, 95125 Catania, Italy
Author to whom correspondence should be addressed.
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)
Full-Text   |   PDF [289 KB, uploaded 8 November 2017]


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
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited (CC BY 4.0).

Share & Cite This Article

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.

Show more citation formats Show less citations formats

Note that from the first issue of 2016, MDPI journals use article numbers instead of page numbers. See further details here.

Article Metrics

Article Access Statistics



[Return to top]
Fractal Fract EISSN 2504-3110 Published by MDPI AG, Basel, Switzerland RSS E-Mail Table of Contents Alert
Back to Top