72 citations · 396 across the 74 of their papers we have counts for
7 papers · 2 filters
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…
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.
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…
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…
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.…