The bessel functions and the hermite polynomials from a unified point of view

2001 ◽  
Vol 80 (3-4) ◽  
pp. 379-384 ◽  
Author(s):  
Giuseppe Dattoli ◽  
Paolo E. Ricci ◽  
Clemente Cesarano
Keyword(s):  
Bessel Functions ◽  
Hermite Polynomials ◽  
Point Of View

scholarly journals The Hermite polynomials and the Bessel functions from a general point of view

2003 ◽  
Vol 2003 (57) ◽  
pp. 3633-3642 ◽  
Author(s):  
G. Dattoli ◽  
H. M. Srivastava ◽  
D. Sacchetti
Keyword(s):  
Difference Equations ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Bessel Functions ◽  
Hermite Polynomials ◽  
Point Of View ◽  
General Point ◽  
Ordinary Case

We introduce new families of Hermite polynomials and of Bessel functions from a point of view involving the use of nonexponential generating functions. We study their relevant recurrence relations and show that they satisfy differential-difference equations which are isospectral to those of the ordinary case. We also indicate the usefulness of some of these new families.

scholarly journals A unified point of view on the theory of generalized Bessel functions

1995 ◽  
Vol 30 (7) ◽  
pp. 113-125 ◽  
Author(s):  
G. Dattoli ◽  
G. Maino ◽  
C. Chiccoli ◽  
S. Lorenzutta ◽  
A. Torre
Keyword(s):  
Bessel Functions ◽  
Point Of View ◽  
Generalized Bessel Functions

Monogenic Generalized Hermite Polynomials and Associated Hermite-Bessel Functions

2010 ◽  
Author(s):  
I. Cação ◽  
Theodore E. Simos ◽  
George Psihoyios ◽  
Ch. Tsitouras
Keyword(s):  
Bessel Functions ◽  
Hermite Polynomials

scholarly journals Generalized Bessel Functions and Generalized Hermite Polynomials

1993 ◽  
Vol 178 (2) ◽  
pp. 509-516 ◽  
Author(s):  
G. Dattoli ◽  
C. Chiccoli ◽  
S. Lorenzutta ◽  
G. Maino ◽  
A. Torre
Keyword(s):  
Bessel Functions ◽  
Hermite Polynomials ◽  
Generalized Bessel Functions

scholarly journals Generalized Dyck tilings (Extended Abstract)

2014 ◽  
Vol DMTCS Proceedings vol. AT,... (Proceedings) ◽  
Author(s):  
Matthieu Josuat-Vergès ◽  
Jang Soo Kim
Keyword(s):  
Hermite Polynomials ◽  
Bruhat Order ◽  
Point Of View ◽  
Weak Order ◽  
Nous Sommes ◽  
Signed Permutations ◽  
Dyck Paths ◽  
Nous Montrons ◽  
International Audience

International audience Recently, Kenyon and Wilson introduced Dyck tilings, which are certain tilings of the region between two Dyck paths. The enumeration of Dyck tilings is related with hook formulas for forests and the combinatorics of Hermite polynomials. The first goal of this work is to give an alternative point of view on Dyck tilings by making use of the weak order and the Bruhat order on permutations. Then we introduce two natural generalizations: $k$-Dyck tilings and symmetric Dyck tilings. We are led to consider Stirling permutations, and define an analogue of the Bruhat order on them. We show that certain families of $k$-Dyck tilings are in bijection with intervals in this order. We enumerate symmetric Dyck tilings and show that certain families of symmetric Dyck tilings are in bijection with intervals in the weak order on signed permutations. Récemment, Kenyon et Wilson ont introduit les pavages de Dyck, qui sont des pavages de la région comprise entre deux chemins de Dyck. L’énumération des pavages de Dyck est reliée aux formules d’équerre sur les forêts et à la combinatoire des polynômes de Hermite. Le premier but de ce travail est de donner un point de vue alternatif sur les pavages de Dyck, en utilisant l’ordre faible et l’ordre de Bruhat sur les permutations. Nous introduisons ensuite deux généralisations naturelles: les $k$-pavages de Dyck et les pavages de Dyck symétriques. Nous sommes amenés àconsidérer les permutations de Stirling, et définissons un analogue de l’ordre de Bruhat. Nous montrons que certaines familles de $k$-pavages de Dyck sont en bijection avec des intervalles de cet ordre. Nous énumérons les pavages de Dyck symétriques et montrons que certaines familles de pavages de Dyck symétriques sont en bijection avec des intervalles de l’ordre faible sur les permutations signées.

scholarly journals Integral and series representations of q-polynomials and functions: Part I

2018 ◽  
Vol 16 (02) ◽  
pp. 209-281 ◽  
Author(s):  
Mourad E. H. Ismail ◽  
Ruiming Zhang
Keyword(s):  
Integral Representation ◽  
Orthogonal Polynomials ◽  
Mellin Transform ◽  
Bessel Functions ◽  
Hermite Polynomials ◽  
Integral Representations ◽  
Moment Problems ◽  
Exponential Functions ◽  
Series Representations ◽  
Indeterminate Moment Problems

By applying an integral representation for [Formula: see text], we systematically derive a large number of new Fourier and Mellin transform pairs and establish new integral representations for a variety of [Formula: see text]-functions and polynomials that naturally arise from combinatorics, analysis, and orthogonal polynomials corresponding to indeterminate moment problems. These functions include [Formula: see text]-Bessel functions, the Ramanujan function, Stieltjes–Wigert polynomials, [Formula: see text]-Hermite and [Formula: see text]-Hermite polynomials, and the [Formula: see text]-exponential functions [Formula: see text], [Formula: see text] and [Formula: see text]. Their representations are in turn used to derive many new identities involving [Formula: see text]-functions and polynomials. In this paper, we also present contour integral representations for the above mentioned functions and polynomials.

scholarly journals The Monomiality Approach to Multi-Index Polynomials in Several Variables

2007 ◽  
Vol 14 (1) ◽  
pp. 53-64
Author(s):  
Carlo Belingeri ◽  
Giuseppe Dattoli ◽  
Paolo E. Ricci
Keyword(s):  
Mixed Type ◽  
Bessel Functions ◽  
Hermite Polynomials ◽  
Generalized Polynomials ◽  
General Technique ◽  
Multi Index ◽  
Several Variables

Abstract The monomiality principle was introduced (see [Dattoli, Hermite–Bessel and Laguerre–Bessel functions: a by-product of the monomiality principle: 147–164, Aracne, 2000] and the references therein) in order to derive the properties of special or generalized polynomials starting from the corresponding ones of monomials. We show a general technique of extending the monomiality approach to multi-index polynomials in several variables. Application of this technique to the case of Hermite, Laguerre-type and mixed-type (i.e., between Laguerre and Hermite) polynomials is given.

Sign in / Sign up

Export Citation Format

Share Document