Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
1.9
Journals
Axioms
Special Issues
Orthogonal Polynomials, Special Functions and Applications: 2nd Edition
share announcement

Orthogonal Polynomials, Special Functions and Applications: 2nd Edition

A special issue of Axioms (ISSN 2075-1680). This special issue belongs to the section "Mathematical Analysis".

Deadline for manuscript submissions: 31 December 2024 | Viewed by 3064

Special Issue Editor

Prof. Dr. Gradimir V. Milovanović

E-Mail Website
Guest Editor
1. Serbian Academy of Sciences and Arts, Kneza Mihaila 35, 11000 Belgrade, Serbia
2. Faculty of Sciences and Mathematics, University of Niš, 18000 Niš, Serbia
Interests: orthogonal polynomials, orthogonal systems and special functions; interpolation, quadrature processes and integral equations; approximations by polynomials, splines and linear operators; numerical and optimization methods; polynomials (extremal problems, inequalities, zeros); iterative processes and inequalities
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue is a continuation of the previous successful Special Issue “Orthogonal Polynomials, Special Functions and Applications”.

Orthogonal polynomials and orthogonal functions, as well as other special functions, are gaining increasing importance and their development is often conditioned by their application in many areas of applied and computational sciences. This Special Issue of Axioms is devoted to various aspects of the theory of orthogonality in real or complex spaces, with respect to the standard inner products (classical and strongly non-classical cases) and moment functionals, including one-dimensional and multidimensional cases, as well as to orthogonalization in numerical linear algebra. Contributions that consider the development and application of special functions, as well as problems in which special functions play a significant role, are welcome. Particularly interesting are the theories and applications in which both orthogonality and special functions are represented. Consideration of the problems in which special functions play a significant role, as well as applications of orthogonal polynomials in approximation theory in the broadest sense, including quadrature formulas and integral equations, will be particularly appreciated. Furthermore,  spectral, collocation and related methods for initial value and initial-boundary value problems that involve PDEs, as well as applications and algorithms for solving open problems in mathematics, physics, and technical sciences, are of interest. Our goal is to gather experts, as well as young researchers focused on the same task, in order to promote and exchange knowledge and improve communication and application. We invite the submission of research papers, as well as review articles.

Prof. Dr. Gradimir V. Milovanović
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 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. Axioms is an international peer-reviewed open access monthly 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 2400 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 and functions
  • orthogonalization in numerical linear algebra
  • special functions
  • hypergeometric functions
  • mittag-leffler functions and generalizations
  • zeros
  • recurrence relations
  • inner products
  • numerical integration
  • quadrature and cubature formulas
  • numerical summation of series
  • numerical differentiation
  • integral equations
  • numerical methods for integral equations and transforms
  • approximation of functions
  • spline approximation
  • padé approximation
  • weighted approximation
  • spectral, collocation and related methods for bvp problems
  • generating functions
  • asymptotics
  • inequalities

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.
  • e-Book format: Special Issues with more than 10 articles can be published as dedicated e-books, ensuring wide and rapid dissemination.

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

Related Special Issue

Published Papers (3 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

17 pages, 354 KiB  
Article
On Voigt-Type Functions Extended by Neumann Function in Kernels and Their Bounding Inequalities
by Rakesh K. Parmar, Tibor K. Pogány and Uthara Sabu
Axioms 2024, 13(8), 534; https://doi.org/10.3390/axioms13080534 - 7 Aug 2024
Viewed by 491
Abstract
The principal aim of this paper is to introduce the extended Voigt-type function Vμ,ν(x,y) and its counterpart extension Wμ,ν(x,y), involving the Neumann function Yν in [...] Read more.
The principal aim of this paper is to introduce the extended Voigt-type function Vμ,ν(x,y) and its counterpart extension Wμ,ν(x,y), involving the Neumann function Yν in the kernel of the representing integral. The newly defined integral reduces to the classical Voigt functions K(x,y) and L(x,y), and to their generalizations by Srivastava and Miller, by the unification of Klusch. Following an approach by Srivastava and Pogány, we also present the multiparameter and multivariable versions Vμ,ν(r)(x,y),Wμ,ν(r)(x,y) and the r positive integer of the initial extensions Vμ,ν(x,y),Wμ,ν(x,y). Several computable series expansions are obtained for the discussed Voigt-type functions in terms of Humbert confluent hypergeometric functions Ψ2(r). Furthermore, by transforming the input extended Voigt-type functions by the Grünwald–Letnikov fractional derivative, we establish representation formulae in terms of the associated Legendre functions of the second kind Qη−ν in the two-parameter and two-variable cases. Finally, functional bounding inequalities are given for Vμ,ν(x,y) and Wμ,ν(x,y). Particularly interesting results are presented for the Neumann function Yν and for the Struve Hν function in the form of several functional bounds. The article ends with a thorough discussion and closing remarks. Full article
(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications: 2nd Edition)
35 pages, 433 KiB  
Article
Some New Families of Finite Orthogonal Polynomials in Two Variables
by Esra Güldoğan Lekesiz and Iván Area
Axioms 2023, 12(10), 932; https://doi.org/10.3390/axioms12100932 - 29 Sep 2023
Viewed by 680
Abstract
In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an infinite family [...] Read more.
In this paper, we generalize the study of finite sequences of orthogonal polynomials from one to two variables. In doing so, twenty three new classes of bivariate finite orthogonal polynomials are presented, obtained from the product of a finite and an infinite family of univariate orthogonal polynomials. For these new classes of bivariate finite orthogonal polynomials, we present a bivariate weight function, the domain of orthogonality, the orthogonality relation, the recurrence relations, the second-order partial differential equations, the generating functions, as well as the parameter derivatives. The limit relations among these families are also presented in Labelle’s flavor. Full article
(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications: 2nd Edition)
14 pages, 316 KiB  
Article
On a Resolution of Another Isolated Case of a Kummer’s Quadratic Transformation for 2F1
by Mohamed Jalel Atia and Ahmed Saleh Al-Mohaimeed
Axioms 2023, 12(2), 221; https://doi.org/10.3390/axioms12020221 - 20 Feb 2023
Cited by 1 | Viewed by 1223
Abstract
It is well-known that the Kummer quadratic transformation formula is valid provided that its parameters fulfill some specific conditions (see Gradshteyn, Ryzhik, Tables of Integrals, Series and Products, 9.130, 9.134.1). Very recently, one of us established a new identity when one of these [...] Read more.
It is well-known that the Kummer quadratic transformation formula is valid provided that its parameters fulfill some specific conditions (see Gradshteyn, Ryzhik, Tables of Integrals, Series and Products, 9.130, 9.134.1). Very recently, one of us established a new identity when one of these conditions is not fulfilled. In this paper, we aim to discuss another isolated case which completely different from the first. Moreover, in the end, we mention two interesting consequences of these two new results. Full article
(This article belongs to the Special Issue Orthogonal Polynomials, Special Functions and Applications: 2nd Edition)
Show export options expand_more Show export options expand_less
Select all
Export citation of selected articles as:
 
Displaying articles 1-3
Back to TopTop