Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.0
2.3
Journals
Mathematics
Special Issues
Polynomial Sequences and Their Applications, 2nd Edition
share announcement

Polynomial Sequences and Their Applications, 2nd Edition

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

Deadline for manuscript submissions: 25 June 2025 | Viewed by 3075

Special Issue Editors

Prof. Dr. Francesco Aldo Costabile

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, Cubo 30/A, 87036 Rende, Italy
Interests: polynomials and their applications in approximation theory; boundary value problems; numerical quadrature; zeros of functions
Special Issues, Collections and Topics in MDPI journals
Prof. Maria I. Gualtieri

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, Cubo 30/A, 87036 Rende, Italy
Interests: polynomials and their applications in approximation theory; boundary value problems; numerical quadrature; zeros of functions
Special Issues, Collections and Topics in MDPI journals
Dr. Anna Napoli

E-Mail Website
Guest Editor
Department of Mathematics and Computer Science, University of Calabria, Via Pietro Bucci, Cubo 30/A, 87036 Rende, Italy
Interests: polynomials and their applications in approximation theory; boundary value problems; numerical quadrature; zeros of functions
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Weierstrass’s Approximation Theorem (1885) is one of the most popular, fundamental, practically important and frequently used theorems in approximation theory. It asserts that every continuous function defined on a closed interval can be uniformly approximated by polynomials. Polynomials are incredibly useful mathematical tools, as they are simply defined and can be calculated quickly on computer systems. They can be differentiated and integrated easily and can be pieced together to form spline curves. Therefore, sequences of polynomials perform an important role in several branches of science: mathematics, physics, engineering, etc. For example, polynomial sequences arise in physics and approximation theory as the solutions of certain ordinary differential equations. Among these, we highlight orthogonal polynomials. In statistics, Hermite polynomials are very important, and they are also orthogonal polynomials. In algebra and combinatorics, umbral polynomials are used, such as rising factorials, falling factorials and Abel, Bell, Bernoulli, Euler, Boile, ciclotomic, Dickson, Fibonacci, Lucas and Touchard polynomials. Some of these belong to special classes, such as Sheffer, Appell and binomial types. For this reason, research in this field appears in different journals/magazines.

A Special Issue that compiles the state of the art of current research will be very useful for the mathematical community.

 Potential topics include but are not limited to the following:

  • Modern umbral calculus (binomial, Appell and Sheffer polynomial sequences)
  • Orthogonal polynomials, matrix orthogonal polynomials, multiple orthogonal polynomials and orthogonal polynomials of several variables
  • Operational methods and the monomiality principle
  • Generating functions of special classes
  • Matrix and determinant approach to special polynomial sequences
  • Applications of special polynomial sequences in approximation theory, in boundary value problems and in quadrature formulas
  • Number theory and special classes of polynomials
  • Asymptotic methods in orthogonal polynomials
  • Fractional calculus
  • Bernstein basis
  • Extrapolation methods

Prof. Dr. Francesco Aldo Costabile
Prof. Maria I. Gualtieri
Dr. Anna Napoli
Guest Editors

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 100 words) can be sent to the Editorial Office for announcement on this website.

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
  • matrix methods
  • monomiality principle
  • generating functions
  • Sheffer, Appell and binomial classes
  • Lidstone type class
  • umbral calculus
  • interpolation
  • boundary value problems
  • numerical quadrature
 
 

Benefits of Publishing in a Special Issue

  • Ease of navigation: Grouping papers by topic helps scholars navigate broad scope journals more efficiently.
  • Greater discoverability: Special Issues support the reach and impact of scientific research. Articles in Special Issues are more discoverable and cited more frequently.
  • Expansion of research network: Special Issues facilitate connections among authors, fostering scientific collaborations.
  • External promotion: Articles in Special Issues are often promoted through the journal's social media, increasing their visibility.
  • Reprint: MDPI Books provides the opportunity to republish successful Special Issues in book format, both online and in print.

Further information on MDPI's Special Issue policies can be found here.

Related Special Issue

Published Papers (5 papers)

Download All Papers
Order results
Result details
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:

Research

18 pages, 490 KiB  
Article
An Orthogonal Polynomial Solution to the Confluent-Type Heun’s Differential Equation
by Saiful R. Mondal and Varun Kumar
Mathematics 2025, 13(8), 1233; https://doi.org/10.3390/math13081233 - 9 Apr 2025
Viewed by 244
Abstract
In this work, we present both analytical and numerical solutions to a seven-parameter confluent Heun-type differential equation. This second-order linear differential equation features three singularities: two regular singularities and one irregular singularity at infinity. First, employing the tridiagonal representation method (TRA), we derive [...] Read more.
In this work, we present both analytical and numerical solutions to a seven-parameter confluent Heun-type differential equation. This second-order linear differential equation features three singularities: two regular singularities and one irregular singularity at infinity. First, employing the tridiagonal representation method (TRA), we derive an analytical solution expressed in terms of Jacobi polynomials. The expansion coefficients of the series are determined as solutions to a three-term recurrence relation, which is satisfied by a modified form of continuous Hahn orthogonal polynomials. Second, we develop a numerical scheme based on the basis functions used in the TRA procedure, enabling the numerical solution of the seven-parameter confluent Heun-type differential equation. Through numerical experiments, we demonstrate the robustness of this approach near singularities and establish its superiority over the finite difference method. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)
►▼ Show Figures

Figure 1

21 pages, 413 KiB  
Article
Construction of a Hybrid Class of Special Polynomials: Fubini–Bell-Based Appell Polynomials and Their Properties
by Yasir A. Madani, Abdulghani Muhyi, Khaled Aldwoah, Amel Touati, Khidir Shaib Mohamed and Ria H. Egami
Mathematics 2025, 13(6), 1009; https://doi.org/10.3390/math13061009 - 20 Mar 2025
Viewed by 246
Abstract
This paper aims to establish a new hybrid class of special polynomials, namely, the Fubini–Bell-based Appell polynomials. The monomiality principle is used to derive the generating function for these polynomials. Several related identities and properties, including symmetry identities, are explored. The determinant representation [...] Read more.
This paper aims to establish a new hybrid class of special polynomials, namely, the Fubini–Bell-based Appell polynomials. The monomiality principle is used to derive the generating function for these polynomials. Several related identities and properties, including symmetry identities, are explored. The determinant representation of the Fubini–Bell-based Appell polynomials is also established. Furthermore, some special members of the Fubini–Bell-based Appell family—such as the Fubini–Bell-based Bernoulli polynomials and the Fubini–Bell-based Euler polynomials—are derived, with analogous results presented for each. Finally, computational results and graphical representations of the zero distributions of these members are investigated. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)
►▼ Show Figures

Figure 1

17 pages, 330 KiB  
Article
Insights into New Generalization of q-Legendre-Based Appell Polynomials: Properties and Quasi Monomiality
by Naeem Ahmad and Waseem Ahmad Khan
Mathematics 2025, 13(6), 955; https://doi.org/10.3390/math13060955 - 13 Mar 2025
Viewed by 365
Abstract
In this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced. These polynomials are studied by means of generating functions, series expansions, and determinant representation. Further, by utilizing the concepts of q-quasi-monomiality, these [...] Read more.
In this paper, by using the zeroth-order q-Tricomi functions, the theory of three-variable q-Legendre-based Appell polynomials is introduced. These polynomials are studied by means of generating functions, series expansions, and determinant representation. Further, by utilizing the concepts of q-quasi-monomiality, these polynomials are examined as several q-quasi-monomial and operational representations; the q-differential equations for the three-variable q-Legendre-based Appell polynomials were obtained. In addition, we established a new generalization of three-variable q-Legendre-Hermite-Appell polynomials, and we derive series expansion, determinant representation, and q-quasi-monomial and q-differential equations. Some examples are framed to better illustrate the theory of three-variable q-Legendre-based Appell polynomials, and this is characterized by the above properties. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)
18 pages, 4885 KiB  
Article
A Study of the q-Truncated Exponential–Appell Polynomials
by Francesco Aldo Costabile, Subuhi Khan and Hassan Ali
Mathematics 2024, 12(23), 3862; https://doi.org/10.3390/math12233862 - 8 Dec 2024
Cited by 3 | Viewed by 942
Abstract
This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp. Appell family along with their graphical representations which contribute to advancing the understanding of q [...] Read more.
This article introduces the 2-variable q-truncated exponential–Appell (q-trunc. exp. Appell) polynomials and investigates their fundamental properties. Specific results are derived for the q-trunc. exp. Appell family along with their graphical representations which contribute to advancing the understanding of q-series and q-special functions. Potential applications of these polynomials span various disciplines, including combinatorics (such as partition theory and combinatorial identities), number theory (such as q-analogues of classical number-theoretic functions), and mathematical physics (such as in quantum groups and statistical mechanics). This study concludes with the introduction of the 2-variable q-trunc. exp. λ-polynomials, thereby broadening the scope and relevance of this research. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)
►▼ Show Figures

Figure A1

16 pages, 291 KiB  
Article
Triple Symmetric Sums of Circular Binomial Products
by Marta Na Chen and Wenchang Chu
Mathematics 2024, 12(15), 2303; https://doi.org/10.3390/math12152303 - 23 Jul 2024
Viewed by 631
Abstract
By employing the generating function approach, 16 triple sums for circular binomial products of binomial coefficients are examined. Recurrence relations and generating functions are explicitly determined. These symmetric sums may find potential applications in the analysis of algorithms, symbolic calculus, and computations in [...] Read more.
By employing the generating function approach, 16 triple sums for circular binomial products of binomial coefficients are examined. Recurrence relations and generating functions are explicitly determined. These symmetric sums may find potential applications in the analysis of algorithms, symbolic calculus, and computations in theoretical physics. Full article
(This article belongs to the Special Issue Polynomial Sequences and Their Applications, 2nd Edition)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-5
Back to TopTop