72 citations · 156 across the 22 of their papers we have counts for
24 papers
Advanced Scientific Methodology Plays Rossini
Silvia Licciardi, Daniela Macchione, Emmanuel Caronna +1
A musical score provides the essential instructions for its performance while containing indications - at times implicit - regarding the composer's intentions. The presence of auth…
Unveiling new perspectives of hypergeometric functions using umbral techniques
Giuseppe Dattoli, Mehnaz Haneef, Subuhi Khan +1
The umbral restyling of hypergeometric functions is shown to be a useful and efficient approach in simplifying the associated computational technicalities. In this article, the aut…
An operational point of view to the theory of multi-variable/multi-index Hermite polynomials
Giuseppe Dattoli, Silvia Licciardi, Elio Sabia
The use of algebraic tools of operational and umbral nature is exploited to develop a new point of view and to extend the theory of Hermite polynomials, with more than one variable…
Hermite, Higher order Hermite, Laguerre type polynomials and Burgers like equations
Giuseppe Dattoli, Roberto Garra, Silvia Licciardi
The multivariable version of ordinary and generalized Hermite polynomials are the natural solutions of the classical heat equation and of its higher order versions. We derive the a…
On an Umbral point of view to the Gaussian and Gaussian like functions
Giuseppe Dattoli, Emanuele Di Palma, Silvia Licciardi
In this note we review the theory of Gaussian functions by exploiting a point of view based on symbolic methods of umbral nature. We introduce quasi-Gaussian functions, which are c…
Monomiality and a New Family of Hermite Polynomials
Giuseppe Dattoli, Silvia Licciardi
In this article we go deeply into the formulation and meaning of the monomiality principle and employ it to study the properties of a set of polynomials, which, asymptotically, red…
On the Evolution of Covid-19 in Italy: a Follow up Note
Giuseppe Dattoli, Emanuele Di Palma, Silvia Licciardi +1
In a previous note we made an analysis of the spreading of the COVID disease in Italy. We used a model based on the logistic and Hubbert functions, the analysis we exploited has sh…
Space Charge and Quantum Corrections in Free Electron Laser Evolution
Giuseppe Dattoli, Hesham Fares, Silvia Licciardi
Effects producing gain dilution in Free Electron Laser devices are well documented. We develop here a unified point of view allowing the introduction of space charge effects, along…
A Note on the Evolution of Covid-19 in Italy
Giuseppe Dattoli, Emanuele Di Palma, Silvia Licciardi +1
We employ methods largely exploited in Physics, in the analysis of the evolution of dynamical systems, to study the pattern of the Covid-19 infection in Italy. The techniques we em…
Umbral-Algebraic Methods and Asymptotic Properties of Special Polynomials
G. Dattoli, S. Licciardi, R. M. Pidatella +1
A new method of algebraic nature is proposed for the study of the asymptotic properties of special polynomials. The technique we foresee is based on the use of umbral operators, al…
Generating Functions for Lacunary Legendre and Legendre-like Polynomials
S. Licciardi, G. Dattoli, R. M. Pidatell
The use of operational methods of different nature is shown to be a fairly powerful tool to study different problems regarding the theory of Legendre and Legendre-like polynomials.…
Operational vs. Umbral Methods and Borel Transform
Giuseppe Dattoli, Silvia Licciardi
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 func…
Repeated derivatives of tanh, sech, ... and associated polynomials
Giuseppe Dattoli, Silvia Licciardi, Rosa Maria Pidatella +1
Elementary problems like the evaluation of repeated derivatives of ordinary transcendent functions can usefully be treated by the use of special polynomials and of a formalism borr…
Dual Numbers and Operational Umbral Methods
Nicolas Behr, Giuseppe Dattoli, Ambra Lattanzi +1
Dual numbers and their higher order version are important tools for numerical computations, and in particular for finite difference calculus. Based upon the relevant algebraic rule…
Operational Methods in the Study of Sobolev-Jacobi Polynomials
Nicolas Behr, Giuseppe Dattoli, Gérard H. E. Duchamp +2
Inspired by ideas from umbral calculus and based on the two types of integrals occurring in the defining equations for the gamma and the reciprocal gamma functions, respectively, w…
Umbral Calculus, a Different Mathematical Language
Silvia Licciardi
This thesis is intended to provide an account of the theory and applications of Operational Methods that allow the "translation" of the theory of special functions and polynomials…
EuPRAXIA@SPARC_LAB Design study towards a compact FEL facility at LNF
M. Ferrario, D. Alesini, M. P. Anania +117
On the wake of the results obtained so far at the SPARC\_LAB test-facility at the Laboratori Nazionali di Frascati (Italy), we are currently investigating the possibility to design…
Comments on the Properties of Mittag-Leffler Function
Giuseppe Dattoli, Katarzyna Gorska, Andrzej Horzela +2
The properties of Mittag-Leffler function is reviewed within the framework of an umbral formalism. We take advantage from the formal equivalence with the exponential function to de…
Umbral Methods and Harmonic Numbers
Giuseppe Dattoli, Bruna Germano, Silvia Licciardi +1
The theory of harmonic based function is discussed here within the framework of umbral operational methods. We derive a number of results based on elementary notions relying on the…
Motzkin Numbers: an Operational Point of View
Marcello Artioli, Giuseppe Dattoli, Silvia Licciardi +1
The Motzkin numbers can be derived as coefficients of hybrid polynomials. Such an identification allows the derivation of new identities for this family of numbers and offers a too…
Theory of Generalized Trigonometric Functions: from Laguerre to Airy Forms
Giuseppe Dattoli, Silvia Licciardi, Rosa Maria Pidatella
We develop a new point of view to introduce families of functions, which can be identified as generalization of the ordinary trigonometric or hyperbolic functions. They are defined…
Hermite Calculus
G. Dattoli, B. Germano, S. Licciardi +1
We develop a new method of umbral nature to treat blocks of Hermite and of Hermite like polynomials as independent algebraic quantities. The Calculus we propose allows the formulat…
Capillary Network, Cancer and Kleiber Law
G. Dattoli, S. Licciardi, C. Guiot +1
We develop a heuristic model embedding Kleiber and Murray laws to describe mass growth, metastasis and vascularization in cancer. We analyze the relevant dynamics using different e…
Products of Bessel functions and associated polynomials
G. Dattoli, E. Di Palma, E. Sabia +1
The symbolic method is used to get explicit formulae for the products or powers of Bessel functions and for the relevant integrals.