33 citations · 86 across the 20 of their papers we have counts for
10 papers · 1 filter
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…
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…
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…
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…
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…
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…