## 16 Citations

### Constructing Bispectral Orthogonal Polynomials from the Classical Discrete Families of Charlier, Meixner and Krawtchouk

- Mathematics
- 2013

Given a sequence of polynomials $$(p_n)_n$$(pn)n, an algebra of operators $${\mathcal A}$$A acting in the linear space of polynomials, and an operator $$D_p\in {\mathcal A}$$Dp∈A with…

### Invariant properties for Wronskian type determinants of classical and classical discrete orthogonal polynomials under an involution of sets of positive integers

- Mathematics
- 2016

Given a finite set $F=\{f_1,\cdots ,f_k\}$ of nonnegative integers (written in increasing size) and a classical discrete family $(p_n)_n$ of orthogonal polynomials (Charlier, Meixner, Krawtchouk or…

### The algebras of difference operators associated to Krall-Charlier orthogonal polynomials

- MathematicsJ. Approx. Theory
- 2018

### The algebras of difference operators associated to Krall–Charlier orthogonal polynomials

- MathematicsJournal of Approximation Theory
- 2018

### Invariance properties of Wronskian type determinants of classical and classical discrete orthogonal polynomials

- MathematicsJournal of Mathematical Analysis and Applications
- 2019

### Bispectrality of Charlier type polynomials

- MathematicsIntegral Transforms and Special Functions
- 2019

ABSTRACT Given a finite set of positive integers G and polynomials , , with degree of equal to g, we associate to them a sequence of Charlier type polynomials defined from the Charlier polynomials by…

### New examples of Krall–Meixner and Krall–Hahn polynomials, with applications to the construction of exceptional Meixner and Laguerre polynomials

- MathematicsJournal of Approximation Theory
- 2021

### On difference operators for symmetric Krall-Hahn polynomials

- MathematicsIntegral Transforms and Special Functions
- 2018

ABSTRACT The problem of finding measures whose orthogonal polynomials are also eigenfunctions of higher-order difference operators have been recently solved by multiplying the classical discrete…

### Exceptional Hahn and Jacobi polynomials with an arbitrary number of continuous parameters

- MathematicsStudies in Applied Mathematics
- 2021

We construct new examples of exceptional Hahn and Jacobi polynomials. Exceptional polynomials are orthogonal polynomials with respect to a measure which are also eigenfunctions of a second‐order…

## References

SHOWING 1-10 OF 27 REFERENCES

### Constructing Bispectral Orthogonal Polynomials from the Classical Discrete Families of Charlier, Meixner and Krawtchouk

- Mathematics
- 2013

Given a sequence of polynomials $$(p_n)_n$$(pn)n, an algebra of operators $${\mathcal A}$$A acting in the linear space of polynomials, and an operator $$D_p\in {\mathcal A}$$Dp∈A with…

### Using D-operators to construct orthogonal polynomials satisfying higher order q-difference equations

- Mathematics
- 2013

### Using D-operators to construct orthogonal polynomials satisfying higher order difference or differential equations

- Mathematics
- 2013

### On a differential equation for Koornwinder's generalized Laguerre polynomials

- Mathematics
- 1991

Koornwinder's generalized Laguerre polynomials {L` N(X)}oo0 are orthogonal on the interval [0, oo) with respect to the weight function 1 f-)xae x + N3(x), (x > -1, N > 0. We show that these…

### Bispectral darboux transformations: An extension of the Krall polynomials

- Mathematics
- 1997

Orthogonal polynomials satisfying fourth order differential equations were classified by H. L. Krall [K2]. They can be obtained from very special instances of the (generalized) Laguerre and the…

### Krall–Laguerre commutative algebras of ordinary differential operators

- Mathematics
- 2013

In 1999, Grünbaum, Haine and Horozov defined a large family of commutative algebras of ordinary differential operators, which have orthogonal polynomials as eigenfunctions. These polynomials are…

### Askey-Wilson type functions with bound states

- Mathematics
- 2006

The two linearly independent solutions of the three-term recurrence relation of the associated Askey-Wilson polynomials, found by Ismail and Rahman in [22], are slightly modified so as to make it…