# Variations around classical orthogonal polynomials. Connected problems

@article{Maroni1993VariationsAC, title={Variations around classical orthogonal polynomials. Connected problems}, author={Pascal Maroni}, journal={Journal of Computational and Applied Mathematics}, year={1993}, volume={48}, pages={133-155} }

## 125 Citations

Modified classical orthogonal polynomials associated with oscillating functions—open problems

- Mathematics
- 1992

A characterization of classical and semiclassical orthogonal polynomials from their dual polynomials

- Mathematics
- 2004

Structure Relations of Classical Orthogonal Polynomials in the Quadratic and q-Quadratic Variable

- MathematicsSymmetry, Integrability and Geometry: Methods and Applications
- 2018

This paper is a contribution to the Special Issue on Orthogonal Polynomials, Special Functions and Applications
(OPSFA14).

The Dω—classical orthogonal polynomials

- Mathematics
- 1997

This is an expository paper; it aims to give an essentially self-contained overview of discrete classical polynomials from their characterizations by Hahn’s property and a Rodrigues’ formula which…

Polynomial sequences associated with the classical linear functionals

- MathematicsNumerical Algorithms
- 2012

This work in mainly devoted to the study of polynomial sequences, not necessarily orthogonal, defined by integral powers of certain first order differential operators in deep connection to the…

SECOND ORDER DIFFERENTIAL-DIFFERENCE EQUATION FOR DUNKL-CLASSICAL ORTHOGONAL POLYNOMIALS

- Mathematics, Philosophy
- 2014

In this paper, we show that Dunkl-classical polynomial sequences can be characterized by a differential-difference equation. AMS Subject Classification: 33C45, 42C05

The Hq-Classical Orthogonal Polynomials

- Mathematics
- 2002

This is an expository paper that aims to give an essentially self-contained survey of a so-called q-analogue of classical polynomials from their characterizations by Hahn's property and a Rodrigues…

On the general cubic decomposition of polynomial sequences

- Mathematics
- 2011

We present the main results about the general cubic decomposition (CD) of polynomial sequences. We deal particularly with the diagonal CD and the CD of orthogonal sequences. This allows us to…

Connection coefficients between orthogonal polynomials and the canonical sequence: an approach based on symbolic computation

- MathematicsNumerical Algorithms
- 2008

A recurrence relation fulfilled by these coefficients and symbolic computation with the Mathematica language is used and the cases of Gegenbauer, Jacobi and a new semi-classical sequence are treated.

## References

SHOWING 1-10 OF 12 REFERENCES

Sur la suite de polynômes orthogonaux associée à la formeu=δc+λ(x−c)−1L

- Mathematics
- 1990

We show that, ifL is regular, semi-classical functional, thenu is also regular and semi-classical for every complex λ, except for a discrete set of numbers depending onL andc. We give the second…

Prolégomènes à l'étude des polynômes orthogonaux semi-classiques

- Mathematics
- 1987

RésuméOn établit une théorie générale des suites de polynômes orthogonaux dont la suite des dérivées est une suite quasi-orthogonale.SummaryOne deals with general theory of orthogonal polynomials…

Another Characterization of the Classical Orthogonal Polynomials

- Mathematics
- 1972

The classical orthogonal polynomials of Jacobi, Laguerre and Hermite are characterized as the only orthogonal polynomials with a differentiation formula of the form \[ \pi (x)P'_n (x) = \left(…

Characterizations of classical polynomials, Portugal. Math

- 1961

Le calcul des formes lineaires et les polynomes orthogonaux semi-classiques

- Orthogonal Polynomials and their Applications,
- 1988