Abstract
Generalized Bessel functions are receiving increasing attention from both the purely mathematical and the applicative points of view. They have, indeed, been shown to be intimately linked to the theory of Jacobi and Weierstrass elliptic functions and offered, in simple and elegant terms, the solutions of problems in electromagnetism, hardly achievable with conventional means. Hermite polynomials with many variables and many indices were originally introduced by Hermite himself. However, unlike the ordinary case, they did not find significant applications and are, therefore, scarcely known to non-mathematicians. Recent developments of phase-space classical and quantum mechanics demand the use of this class of orthogonal polynomial and for the associated orthornormal functions. The theory of generalized Bessel functions and generalized Hermite polynomials from a unified point of view are discussed. New addition and multiplication theorems for the multivariable Bessel functions as well as the set of partial differential equations they satisfy are presented. As to the Hermite polynomials, the relevant formalism is discussed and the generalised harmonic oscillator functions along with the relevant creation and annihilation operators are introduced. Some comments on the applications are also presented.
Dattoli, G;
Torre, A;
[1]
Lorenzutta, S;
Maino, G
[2]
- ENEA, Frascati (Italy). Centro Ricerche Energia - Area Energia e Innovazione
- ENEA, Bologna (Italy). Centro Ricerche Energia `E. Clementel` - Area Energia e Innovazione
Citation Formats
Dattoli, G, Torre, A, Lorenzutta, S, and Maino, G.
Generalized forms of Bessel functions and Hermite polynomials.
Italy: N. p.,
1994.
Web.
Dattoli, G, Torre, A, Lorenzutta, S, & Maino, G.
Generalized forms of Bessel functions and Hermite polynomials.
Italy.
Dattoli, G, Torre, A, Lorenzutta, S, and Maino, G.
1994.
"Generalized forms of Bessel functions and Hermite polynomials."
Italy.
@misc{etde_10123667,
title = {Generalized forms of Bessel functions and Hermite polynomials}
author = {Dattoli, G, Torre, A, Lorenzutta, S, and Maino, G}
abstractNote = {Generalized Bessel functions are receiving increasing attention from both the purely mathematical and the applicative points of view. They have, indeed, been shown to be intimately linked to the theory of Jacobi and Weierstrass elliptic functions and offered, in simple and elegant terms, the solutions of problems in electromagnetism, hardly achievable with conventional means. Hermite polynomials with many variables and many indices were originally introduced by Hermite himself. However, unlike the ordinary case, they did not find significant applications and are, therefore, scarcely known to non-mathematicians. Recent developments of phase-space classical and quantum mechanics demand the use of this class of orthogonal polynomial and for the associated orthornormal functions. The theory of generalized Bessel functions and generalized Hermite polynomials from a unified point of view are discussed. New addition and multiplication theorems for the multivariable Bessel functions as well as the set of partial differential equations they satisfy are presented. As to the Hermite polynomials, the relevant formalism is discussed and the generalised harmonic oscillator functions along with the relevant creation and annihilation operators are introduced. Some comments on the applications are also presented.}
place = {Italy}
year = {1994}
month = {Jun}
}
title = {Generalized forms of Bessel functions and Hermite polynomials}
author = {Dattoli, G, Torre, A, Lorenzutta, S, and Maino, G}
abstractNote = {Generalized Bessel functions are receiving increasing attention from both the purely mathematical and the applicative points of view. They have, indeed, been shown to be intimately linked to the theory of Jacobi and Weierstrass elliptic functions and offered, in simple and elegant terms, the solutions of problems in electromagnetism, hardly achievable with conventional means. Hermite polynomials with many variables and many indices were originally introduced by Hermite himself. However, unlike the ordinary case, they did not find significant applications and are, therefore, scarcely known to non-mathematicians. Recent developments of phase-space classical and quantum mechanics demand the use of this class of orthogonal polynomial and for the associated orthornormal functions. The theory of generalized Bessel functions and generalized Hermite polynomials from a unified point of view are discussed. New addition and multiplication theorems for the multivariable Bessel functions as well as the set of partial differential equations they satisfy are presented. As to the Hermite polynomials, the relevant formalism is discussed and the generalised harmonic oscillator functions along with the relevant creation and annihilation operators are introduced. Some comments on the applications are also presented.}
place = {Italy}
year = {1994}
month = {Jun}
}