72 citations · 396 across the 74 of their papers we have counts for
16 papers · 1 filter
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…
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.…
Can Umbral and -calculus be merged?
G. Dattoli, B. Germano, K. Górska +1
The -calculus is reformulated in terms of the umbral calculus and of the associated operational formalism. We show that new and interesting elements emerge from such a restyling…
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…
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…
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…
Operational versus umbral methods and the Borel transform
G. Dattoli, E. Di Palma, E. Sabia +3
Integro-differential methods, currently exploited in calculus, provide an inexhaustible source of tools to be applied to a wide class of problems, involving the theory of special f…
The spherical Bessel and Struve functions and operational methods
D. Babusci, G. Dattoli, K. Gorska +1
We review some aspects of the theory of spherical Bessel functions and Struve functions by means of an operational procedure essentially of umbral nature, capable of providing the…
Chebyshev polynomials and generalized complex numbers
D. Babusci, G. Dattoli, E. Di Di Palma +1
The generalized complex numbers can be realized in terms of or higher-order matrices and can be exploited to get different ways of looking at the trigonometric functions…
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…
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…
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…