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

@article{Durn2013UsingDT,
  title={Using D-operators to construct orthogonal polynomials satisfying higher order difference or differential equations},
  author={Antonio J. Dur{\'a}n},
  journal={Journal of Approximation Theory},
  year={2013},
  volume={174},
  pages={10-53}
}
  • A. J. Durán
  • Published 4 February 2013
  • Mathematics
  • Journal of Approximation Theory

On difference operators for symmetric Krall-Hahn polynomials

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

Symmetric differential operators for Sobolev orthogonal polynomials of Laguerre- and Jacobi-type

  • C. Markett
  • Mathematics
    Integral Transforms and Special Functions
  • 2021
ABSTRACT The Laguerre-Sobolev polynomials form an orthogonal polynomial system on the positive half-line with respect to the classical Laguerre measure with parameter and, in general, two point

Differential equations for discrete Jacobi–Sobolev orthogonal polynomials

The aim of this paper is to study differential properties of orthogonal polynomials with respect to a discrete Jacobi-Sobolev bilinear form with mass point at −1 and/or +1. In particular, we

Bispectrality of Charlier type polynomials

  • A. J. Durán
  • Mathematics
    Integral 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

Symmetries for Casorati determinants of classical discrete orthogonal polynomials

Abstract. Given a classical discrete family (pn)n of orthogonal polynomials (Charlier, Meixner, Krawtchouk or Hahn) and the set of numbers m + i − 1, i = 1, · · · , k and k,m ≥ 0, we consider the k ×

On the higher-order differential equations for the generalized Laguerre polynomials and Bessel functions

  • C. Markett
  • Mathematics
    Integral Transforms and Special Functions
  • 2019
ABSTRACT In the enduring, fruitful research on spectral differential equations with polynomial eigenfunctions, Koornwinder's generalized Laguerre polynomials are playing a prominent role. Being

References

SHOWING 1-10 OF 37 REFERENCES

A method of constructing Krall's polynomials

Bispectral darboux transformations: An extension of the Krall polynomials

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

On orthogonal polynomials spanning a non-standard flag

We survey some recent developments in the theory of orthogonal polynomials defined by differential equations. The key finding is that there exist orthogonal polynomials defined by 2nd order

Symmetries for Casorati determinants of classical discrete orthogonal polynomials

Abstract. Given a classical discrete family (pn)n of orthogonal polynomials (Charlier, Meixner, Krawtchouk or Hahn) and the set of numbers m + i − 1, i = 1, · · · , k and k,m ≥ 0, we consider the k ×

AN APPLICATION OF A NEW THEOREM ON ORTHOGONAL POLYNOMIALS AND DIFFERENTIAL EQUATIONS

Abstract Recently this author proved that if an OPS satisfies a differential equation of the form then, under certain conditions, an orthogonalizing weight distribution can be found that

Orthogonal Polynomials Satisfying Higher-Order Difference Equations

We introduce a large class of measures with orthogonal polynomials satisfying higher-order difference equations with coefficients independent of the degree of the polynomials. These measures are

Classical Orthogonal Polynomials of a Discrete Variable

The basic properties of the polynomials p n (x) that satisfy the orthogonality relations $$ \int_a^b {{p_n}(x)} {p_m}(x)\rho (x)dx = 0\quad (m \ne n) $$ (2.0.1) hold also for the polynomials