On structure formulas for Wilson polynomials

Sadjang, P. Njionou; Koepf, Wolfram; Foupouagnigni, M.

doi:10.1080/10652469.2015.1076408

Search citation statements

Order By: Relevance

Paper Sections

Select...

The Little Q-laguerre Functions1

Conclusion and Further Perspectives1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2022

Publication Types

Select...

Article5

Book1

Relationship

Self Cite2

Independent4

Authors

Journals

Cited by 7 publications

(3 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Thus, using the definitions of the fractional Little q-Laguerre functions and the fractional q-derivative (21), combined with the transformations (4) and (6) we have:…”

Section: The Little Q-laguerre Functionsmentioning

confidence: 99%

See 1 more Smart Citation

On Fractional q-Extensions of Some q-Orthogonal Polynomials

Sadjang

Mboutngam

2020

Axioms

View full text Add to dashboard Cite

In this paper, we introduce a fractional q-extension of the q-differential operator Dq−1 and prove some of its main properties. Next, fractional q-extensions of some classical q-orthogonal polynomials are introduced and some of the main properties of the newly-defined functions are given. Finally, a fractional q-difference equation of Gaussian type is introduced and solved by means of the power series method.

show abstract

“…Thus, using the definitions of the fractional Little q-Laguerre functions and the fractional q-derivative (21), combined with the transformations (4) and (6) we have:…”

Section: The Little Q-laguerre Functionsmentioning

confidence: 99%

“…As future works, we plan to provide similar extensions to classical orthogonal polynomials on quadratic and q-quadratic lattices. To do it, it will be necessary to introduce new differential operators of fractional order, namely, the Wilson operator [11,21]…”

Section: Conclusion and Further Perspectivesmentioning

confidence: 99%

On Fractional q-Extensions of Some q-Orthogonal Polynomials

Sadjang

Mboutngam

2020

Axioms

View full text Add to dashboard Cite

show abstract

“…(See[27]) The operators D and S satisfy the following product rulesD(fg) = Df Sg + Sf Dg,(2.5) S(fg) = −x 2 Df Dg + Sf Sg,…”

mentioning

confidence: 99%

On Non-linear Characterizations of Classical Orthogonal Polynomials

et al. 2022

Self Cite

View full text Add to dashboard Cite

Classical orthogonal polynomials are known to satisfy seven equivalent properties, namely the Pearson equation for the linear functional, the second-order differential/difference/q-differential/ divided-difference equation, the orthogonality of the derivatives, the Rodrigues formula, two types of structure relations, and the Riccati equation for the formal Stieltjes function. In this work, following previous work by Kil et al. (J Differ Equ Appl 4:145–162, 1998a; Kyungpook Math J 38:259–281, 1998b), we state and prove a non-linear characterization result for classical orthogonal polynomials on non-uniform lattices. Next, we give explicit relations for some families of these classes.

show abstract

Orthogonal Polynomials and Computer Algebra

Koepf¹

2020

Orthogonal Polynomials

View full text Add to dashboard Cite

On structure formulas for Wilson polynomials

Cited by 7 publications

References 12 publications

On Fractional q-Extensions of Some q-Orthogonal Polynomials

On Fractional q-Extensions of Some q-Orthogonal Polynomials

On Non-linear Characterizations of Classical Orthogonal Polynomials

Orthogonal Polynomials and Computer Algebra

Contact Info

Product

Resources

About