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Mathematics
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Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications
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Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications

A special issue of Mathematics (ISSN 2227-7390). This special issue belongs to the section "E: Applied Mathematics".

Deadline for manuscript submissions: 20 May 2026 | Viewed by 2606

Special Issue Editor

Prof. William Ramirez

E-Mail Website
Guest Editor
1. Department of Natural and Exact Sciences, Universidad de la Costa, Calle 58, 55-66, Barranquilla 080002, Colombia
2. Section of Mathematics, UniNettuno University, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy
Interests: harmonic analysis; orthogonal polynomials; special functions

Special Issue Information

Dear Colleagues,

Harmonic analysis, orthogonal polynomials, special functions, and fractional calculus are well-established fields of research within the mathematical sciences. Over the centuries, these areas have evolved into classical disciplines, enriched by pioneering contributions that have introduced innovative methodologies and provided in-depth insights into both theoretical and applied problems.

The objective of this Special Issue, “Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications”, is to present recent trends, novel methodologies, and significant applications in these fields.

Prof. William Ramirez
Guest Editor

Manuscript Submission Information

Manuscripts should be submitted online at www.mdpi.com by registering and logging in to this website. Once you are registered, click here to go to the submission form. Manuscripts can be submitted until the deadline. All submissions that pass pre-check are peer-reviewed. Accepted papers will be published continuously in the journal (as soon as accepted) and will be listed together on the special issue website. Research articles, review articles as well as short communications are invited. For planned papers, a title and short abstract (about 250 words) can be sent to the Editorial Office for assessment.

Submitted manuscripts should not have been published previously, nor be under consideration for publication elsewhere (except conference proceedings papers). All manuscripts are thoroughly refereed through a single-blind peer-review process. A guide for authors and other relevant information for submission of manuscripts is available on the Instructions for Authors page. Mathematics is an international peer-reviewed open access semimonthly journal published by MDPI.

Please visit the Instructions for Authors page before submitting a manuscript. The Article Processing Charge (APC) for publication in this open access journal is 2600 CHF (Swiss Francs). Submitted papers should be well formatted and use good English. Authors may use MDPI's English editing service prior to publication or during author revisions.

Keywords

  • orthogonal polynomials
  • harmonic analysis
  • fractional calculus
  • applied mathematics
  • special functions and applied mathematics

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Published Papers (4 papers)

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Research

20 pages, 1610 KB  
Article
Exploring a Novel Family of Appell Polynomials Associated with Gould–Hopper–Fubini Polynomials
by F. Gassem, Abdulghani Muhyi, Hadeel Arwah, Habeeb Ibrahim, Khaled Aldwoah, Amer Alsulami and Mohammed Rabih
Mathematics 2026, 14(5), 791; https://doi.org/10.3390/math14050791 - 26 Feb 2026
Viewed by 458
Abstract
In this paper, we establish a new hybrid class of special polynomials, the Gould–Hopper–Fubini-based Appell polynomials. Using the monomiality principle, we derive their generating function and explore related properties and identities. We also investigate symmetry identities and obtain a determinant representation for these [...] Read more.
In this paper, we establish a new hybrid class of special polynomials, the Gould–Hopper–Fubini-based Appell polynomials. Using the monomiality principle, we derive their generating function and explore related properties and identities. We also investigate symmetry identities and obtain a determinant representation for these polynomials. Finally, we present and discuss results for several special cases of this family and support the derived results with computational studies and visual representations. Full article
(This article belongs to the Special Issue Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications)
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23 pages, 464 KB  
Article
Approximation Associated with Kantorovich Version of Bézier (λ,q)–Bernstein–Schurer Operators
by Md. Nasiruzzaman, Mohammad Farid, Harun Çiçek and Nadeem Rao
Mathematics 2026, 14(4), 644; https://doi.org/10.3390/math14040644 - 12 Feb 2026
Viewed by 369
Abstract
In the present paper, the Kantorovich modification of the Schurer type of (λ,q)-Bernstein operators, which are associated by the shape parameter −1≤λ≤1 and the Bézier basis function, is presented. Using Korovkin’s theorem, we [...] Read more.
In the present paper, the Kantorovich modification of the Schurer type of (λ,q)-Bernstein operators, which are associated by the shape parameter −1≤λ≤1 and the Bézier basis function, is presented. Using Korovkin’s theorem, we establish several local and global approximation properties. Lastly, we calculate the convergence properties for the functions that belong to Peetre’s K-functional and Lipschitz maximum by using the classical modulus of continuity and second-order modulus of continuity. In the last section, graphical and numerical analysis are studied. Full article
(This article belongs to the Special Issue Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications)
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30 pages, 405 KB  
Article
Some Novel Formulas of the Telephone Polynomials Including New Definite and Indefinite Integrals
by Omar Mazen Alqubori and Waleed Mohamed Abd-Elhameed
Mathematics 2026, 14(3), 448; https://doi.org/10.3390/math14030448 - 27 Jan 2026
Cited by 1 | Viewed by 509
Abstract
In this article, we present new theoretical findings on specific polynomials that generalize the concept of telephone numbers, namely, Telephone polynomials (TelPs). Several new formulas are developed, including expressions for higher-order derivatives, repeated integrals, and moment formulas of TelPs. Moreover, we derive explicit [...] Read more.
In this article, we present new theoretical findings on specific polynomials that generalize the concept of telephone numbers, namely, Telephone polynomials (TelPs). Several new formulas are developed, including expressions for higher-order derivatives, repeated integrals, and moment formulas of TelPs. Moreover, we derive explicit connections between the derivatives of TelPs and the two classes of symmetric and non-symmetric polynomials, producing many formulas between these polynomials and several celebrated polynomials such as Hermite, Laguerre, Jacobi, Fibonacci, Lucas, Bernoulli, and Euler polynomials. The inverse formulas are also obtained, expressing the derivatives of well-known polynomial families in terms of TelPs. Furthermore, some novel linearization formulas (LFs) with some classes of polynomials are established. Finally, some new definite and indefinite integrals of TelPs are established using some of the developed relations. Full article
(This article belongs to the Special Issue Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications)
17 pages, 631 KB  
Article
A New Modification of Baskakov–Schurer–Stancu Operators: Weighted and Pointwise Approximation Theories
by Nadire Fulda Odabaşı, Mohammad Farid, Nadeem Rao and Reşat Aslan
Mathematics 2026, 14(2), 241; https://doi.org/10.3390/math14020241 - 8 Jan 2026
Cited by 2 | Viewed by 523
Abstract
The behavior of a new modification of operators of the Baskakov–Schurer–Stancu variant is discussed in this study. First, we establish certain necessary moment and central moment estimates. We then demonstrate the weighted approximation result of the suggested operators using a Korovkin-type theorem in [...] Read more.
The behavior of a new modification of operators of the Baskakov–Schurer–Stancu variant is discussed in this study. First, we establish certain necessary moment and central moment estimates. We then demonstrate the weighted approximation result of the suggested operators using a Korovkin-type theorem in weighted spaces. We also give the rate at which these operators converge. Next, we establish theorems of pointwise convergence. Finally, we show several graphical representations to illustrate the accuracy and functionality of the operators. Full article
(This article belongs to the Special Issue Recent Advances in Orthogonal Polynomials, Special Functions, and Their Applications)
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