# On the functional equation for classical orthogonal polynomials on lattices

@inproceedings{Castillo2021OnTF, title={On the functional equation for classical orthogonal polynomials on lattices}, author={Kenier Castillo and Duclaire Mbouna and J. Petronilho}, year={2021} }

Necessary and sufficient conditions for the regularity of solutions of the functional equation appearing in the theory of classical orthogonal polynomials on lattices are stated. Moreover, the functional Rodrigues formula and a closed formula for the recurrence coefficients are presented.

#### One Citation

A characterization of continuous $q$-Jacobi, Chebyshev of the first kind and Al-Salam Chihara polynomials

- Mathematics
- 2021

The purpose of this note is to characterize those orthogonal polynomials sequences (Pn)n≥0 for which π(x)DqPn(x) = (anx+ bn)Pn(x) + cnPn−1(x), n = 0, 1, 2, . . . , where Dq is the Askey-Wilson…

#### References

SHOWING 1-10 OF 28 REFERENCES

On moments of classical orthogonal polynomials

- Mathematics
- 2015

Abstract In this work, using the inversion coefficients and some connection coefficients between some polynomial sets, we give explicit representations of the moments of all the orthogonal…

Characterization theorem for classical orthogonal polynomials on non-uniform lattices: the functional approach

- Mathematics
- 2011

Using the functional approach, we state and prove a characterization theorem for classical orthogonal polynomials on non-uniform lattices (quadratic lattices of a discrete or a q-discrete variable)…

Classical orthogonal polynomials

- Mathematics
- 1985

There have been a number of definitions of the classical orthogonal polynomials, but each definition has left out some important orthogonal polynomials which have enough nice properties to justify…

On classical orthogonal polynomials related to Hahn's operator

- Mathematics
- 2019

ABSTRACT Let be a non-zero linear functional acting on the space of polynomials. Let be a Hahn operator acting on the dual space of polynomials. Suppose that there exist polynomials φ and ψ, with and…

On the solution of some distributional differential equations: existence and characterizations of the classical moment functionals

- Mathematics
- 1994

Given two polynomials φ and ψ such that deg φ ≤ 2 and deg ψ = 1, and a continuous linear functional U (defined on the space of all polynomials with complex coefficients) which is a solution of the…

On the modifications of semi-classical orthogonal polynomials on nonuniform lattices

- Mathematics
- 2017

Abstract Semi classical orthogonal polynomials on nonuniform lattices with respect to a linear functional L are defined as polynomials ( P n ) where the degree of P n is exactly n, the P n satisfy…

The theory of difference analogues of special functions of hypergeometric type

- Mathematics
- 1989

CONTENTS Introduction ??1. Preliminary information ??2. Construction of particular solutions for a difference equation of hypergeometric type on non-uniform lattices ??3. Some properties of…

Hypergeometric Orthogonal Polynomials and Their q-Analogues

- Mathematics
- 2010

Definitions and Miscellaneous Formulas.- Classical orthogonal polynomials.- Orthogonal Polynomial Solutions of Differential Equations.- Orthogonal Polynomial Solutions of Real Difference Equations.-…

Orthogonal Polynomials and Special Functions

- Mathematics
- 1975

Asymptotics of Jacobi matrices for a family of fractal measures GÖKALP APLAN BILKENT UNIVERSITY, TYRKEY There are many results concerning asymptotics of orthogonal polynomials and Jacobi matrices…

Classical and quantum orthogonal polynomials in one variable

- Mathematics
- 2008

Feel like writing a review for The Mathematical Intelligencer? You are welcome to submit an unsolicited review of a book of your choice; or, if you would welcome being assigned a book to review,…