Orthogonal Polynomials, Special Functions and Applications II

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

Deadline for manuscript submissions: 30 June 2024 | Viewed by 2204

Special Issue Editor


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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
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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

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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

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Published Papers (2 papers)

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Research

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 580
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 II)
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 1108
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 II)
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