33 citations · 86 across the 20 of their papers we have counts for
21 papers
A novel advancement in the study of Appell polynomials via Padè rational approximants
Giuseppe Dattoli, Subuhi Khan, Ujair Ahmad
The use of approximants of Padè type are employed to develop a method aimed at opening new perspectives in the theory of Appell polynomials , specified by the generating fu…
Higher-order Hermite numbers: Properties and applications to evolution problems
Giuseppe Dattoli, Subuhi Khan, Ujair Ahmad
The operational calculus associated with Hermite numbers has been shown to be an effective tool for simplifying the study of special functions. Within this context, Hermite polynom…
Nearly cosine series and generalized trigonometric functions
A. Curcio, G. Dattoli, E. Di Palma +2
A class of overlooked trigonometric-like functions is explored in this article, along with the relevant applications in applications. We show indeed that Taylor series, resembling…
A note on exact results for Burgers-like equations involving Laguerre derivatives
Giuseppe Dattoli, Riccardo Droghei, Roberto Garra
In this note, we consider some Burgers-like equations involving Laguerre derivatives and demonstrate that it is possible to construct specific exact solutions using separation of v…
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…
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…
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…
Laser Heater and seeded Free Electron Laser
G. Dattoli, V. Petrillo, E. Sabia
In this paper we consider the effect of laser heater on a seeded Free Electron Laser. We develop a model embedding the effect of the energy modulation induced by the heater with th…
IRIDE White Book, An Interdisciplinary Research Infrastructure based on Dual Electron linacs&lasers
D. Alesini, M. Alessandroni, M. P. Anania +211
This report describes the scientific aims and potentials as well as the preliminary technical design of IRIDE, an innovative tool for multi-disciplinary investigations in a wide fi…
Lacunary Generating Functions for the Laguerre Polynomials
D. Babusci, G. Dattoli, K. Gorska +1
Symbolic methods of umbral nature play an important and increasing role in the theory of special functions and in related fields like combinatorics. We discuss an application of th…
On Mittag-Leffler function and associated polynomials
D. Babusci, G. Dattoli, K. Górska
The Mittag-Leffler function plays a role of central importance in the theory of fractional derivatives. In this brief note we discuss the properties of this function and its connec…
SASE FEL Storage Ring
G. Dattoli, E. Di Palma, A. Petralia +1
We explore the possibility of operating a SASE FEL with a Storage Ring. We use a semi-analytical model to obtain the evolution inside the undulator by taking into account the inter…
Symbolic calculus and integrals of Laguerre polynomials
D. Babusci, G. Dattoli, K. Górska
An umbral type formalism is used to derive integrals involving products of Laguerre polynomials and other special functions.
The Ramanujan master theorem and its implications for special functions
K. Gorska, D. Babusci, G. Dattoli +2
We study a number of possible extensions of the Ramanujan master theorem, which is formulated here by using methods of Umbral nature. We discuss the implications of the procedure f…
Operational methods and Lorentz-type equations of motion
D. Babusci, G. Dattoli, E. Sabia
We propose an operational method for the solution of differential equations involving vector products. The technique we propose is based on the use of the evolution operator, defin…
The Euler Legacy to Modern Physics
G. Dattoli, M. Del Franco
Particular families of special functions, conceived as purely mathematical devices between the end of XVIII and the beginning of XIX centuries, have played a crucial role in the de…
Generalization of the Airy function and the operational methods
D. Babusci, G. Dattoli, D. Sacchetti
In this brief note the operatorial methods are applied to the study of the Airy function and its generalizations.
Integral equations, fractional calculus and shift operator
D. Babusci, G. Dattoli, D. Sacchetti
We present an extension of a previously developed method employing the formalism of the fractional derivatives to solve new classes of integral equations. This method uses differen…
The Pseudo-Hyperbolic Functions and the Matrix Representation of Eisenstein Complex Numbers
G. Dattoli, E. Sabia, M. Del Franco
We consider the matrix representation of the Eisenstein numbers and in this context we discuss the theory of the Pseudo Hyperbolic Functions. We develop a geometrical interpretatio…