72 citations · 396 across the 74 of their papers we have counts for
15 papers · 1 filter
Umbral methods and operator ordering
D. Babusci, G. Dattoli
By using methods of umbral nature, we discuss new rules concerning the operator ordering. We apply the technique of formal power series to take advantage from the wealth of propert…
On evaluation of integrals involving Bessel functions
D. Babusci, G. Dattoli
We introduce a symbolic method for the evaluation of definite integrals containing combinations of various functions, including exponentials, logarithm and products of Bessel funct…
Integrals of Bessel functions
D. Babusci, G. Dattoli, B. Germano +2
We use the operator method to evaluate a class of integrals involving Bessel or Bessel-type functions. The technique we propose is based on the formal reduction of these family of…
Operator solutions for fractional Fokker-Planck equations
K. Gorska, K. A. Penson, D. Babusci +2
We obtain exact results for fractional equations of Fokker-Planck type using evolution operator method. We employ exact forms of one-sided Levy stable distributions to generate a s…
The algebra of factorial polynomials
D. Babusci, G. Dattoli, M. Carpanese
We discuss the formal aspects of the factorial polynomials and of the associated series. We develop the theory using the formalism of quasi-monomials and prove the usefulness of th…
On the logarithm of the derivative operator
D. Babusci, G. Dattoli
We study the properties of the logarithm of the derivative operator and show that its action on a constant is not zero, but yields the sum of the logarithmic function and the Euler…
A note on the extension of the Dirac method
D. Babusci, G. Dattoli, M. Quattromini +1
In this note we extend the Dirac method to partial differential equations involving higher order roots of differential operators.
On Ramanujan Master Theorem
D. Babusci, G. Dattoli
In this short note we use the umbral formalism to derive the Ramanujan Master Theorem and discuss its extension to more general cases.
Complex-type numbers and generalizations of the Euler identity
D. Babusci, G. Dattoli, E. Di Palma +1
We consider different generalizations of the Euler formula and discuss the properties of the associated trigonometric functions. The problem is analyzed from different points of vi…
On integrals involving Hermite polynomials
D. Babusci, G. Dattoli, M. Quattromini
We show how the combined use of the generating function method and of the theory of multivariable Hermite polynomials is naturally suited to evaluate integrals of gaussian function…
Fel Oscillators with Tapered Undulators: Inclusion of Harmonic Generation and Pulse Propagation
G. Dattoli, P. L. Ottaviani, S. Pagnutti +1
We review the theory of FEL oscillators operating with tapered undulators. We consider the case of a uniform tapering and introduce a parameter which characterizes the effect of th…
The Parabolic-Trigonometric Functions
G. Dattoli, M. Migliorati, M. Quattromini +1
The parabolic functions are introduced in analogy to the circular and hyperbolic cases. We discuss the relevant properties, the geometrical interpretation and touch on possible gen…
The parabolic trigonometric functions and the Chebyshev radicals
G. Dattoli, M. Migliorati, P. E. Ricci
The parabolic trigonometric functions have recently been introduced as an intermediate step between circular and hyperbolic functions. They have been shown to be expressible in ter…
Slices and Ellipse Geometry
G. Dattoli, E. Sabia, M. Del Franco +1
We discuss the new problems emerging in charged beam transport for SASE FEL dynamics. The optimization of the magnetic transport system for future devices requires new concepts ass…
Relativistic equations with fractional and pseudo-differential operators
D. Babusci, G. Dattoli, M. Quattromini
In this paper we use different techniques from the fractional and pseudo-operators calculus to solve partial differential equations involving operators with non integer exponents.…