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Journals
Axioms
Special Issues
Research in Special Functions
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Research in Special Functions

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

Deadline for manuscript submissions: 28 February 2025 | Viewed by 6274

Special Issue Editors

Prof. Dr. Ilya Shilin

E-Mail Website
Guest Editor
1. Department of Higher Mathematics, National Research University MPEI, Moscow 111250, Russia
2. Department of Algebra, Moscow State Pedagogical University, Moscow 119991, Russia
Interests: special functions of mathematical physics; group theoretical approach to special functions; integral transforms
Special Issues, Collections and Topics in MDPI journals
Prof. Dr. Junesang Choi

E-Mail Website
Guest Editor
Department of Mathematics, Dongguk University, Wise Campus, Gyeongju 38066, Republic of Korea
Interests: special functions; analytic number theory; fractional calculus
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

This Special Issue aims to present novel results for special functions arising in various areas of contemporary mathematics, including mathematical physics, theory of ODE and PDE, number theory, discrete mathematics, harmonic analysis, theory of integral transforms, Lie groups and Lie algebras representation theory, q-calculus, fractional calculus, etc. We expect that this Special Issue will address both classical special functions and their numerous extensions, including q-analogues, fractional analogues, and hyper (multi-index) analogues.

We look forward to receiving your contributions including new properties, integrals, series and recurrent relations, formulas for asymptotic behavior and values of integral operators, new results for analytic continuations, etc. We invite authors to present new theorems describing connections between special functions of mathematical physics and their q-analogues with classical Lie groups and algebras and quantum groups and Hopf algebras, respectively.

We are also interested in various applications of special functions, since “A function is a special function if it occurs often enough so that it gets a name” (Richard Askey). 

You may choose our Joint Special Issue in Symmetry.

Prof. Dr. Ilya Shilin
Prof. Dr. Junesang Choi
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. 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

  • special functions
  • hyperfunction
  • q-special functions
  • special functions of fractional calculus
  • group theoretical approach to special functions
  • harmonic analysis
  • special functions of number theory
  • generalized hypergeometric function
  • special functions of several variables
  • generalized fractional integrals and fractional derivatives

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

Published Papers (5 papers)

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Research

18 pages, 319 KiB  
Article
Harmonic Series with Multinomial Coefficient 4nn,n,n,n and Central Binomial Coefficient 2nn
by Chunli Li and Wenchang Chu
Axioms 2024, 13(7), 434; https://doi.org/10.3390/axioms13070434 - 27 Jun 2024
Viewed by 545
Abstract
Classical hypergeometric series are reformulated as analytic functions of their parameters (in both the numerator and the denominator). Then, the coefficient extraction method is applied to examine hypergeometric series transformations. Several new closed form evaluations are established for harmonic series containing multinomial coefficient [...] Read more.
Classical hypergeometric series are reformulated as analytic functions of their parameters (in both the numerator and the denominator). Then, the coefficient extraction method is applied to examine hypergeometric series transformations. Several new closed form evaluations are established for harmonic series containing multinomial coefficient 4nn,n,n,n and central binomial coefficient 2nn. These results exclusively concern the alternating series of convergence rate “−1/4”. Full article
(This article belongs to the Special Issue Research in Special Functions)
15 pages, 299 KiB  
Article
On the Two-Variable Analogue Matrix of Bessel Polynomials and Their Properties
by Ahmed Bakhet, Shahid Hussain, Mohamed Niyaz, Mohammed Zakarya and Ghada AlNemer
Axioms 2024, 13(3), 202; https://doi.org/10.3390/axioms13030202 - 17 Mar 2024
Cited by 1 | Viewed by 1218
Abstract
In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present [...] Read more.
In this paper, we explore a study focused on a two-variable extension of matrix Bessel polynomials. We initiate the discussion by introducing the matrix Bessel polynomials involving two variables and derive specific differential formulas and recurrence relations associated with them. Additionally, we present a segment detailing integral formulas for the extended matrix Bessel polynomials. Lastly, we introduce the Laplace–Carson transform for the two-variable matrix Bessel polynomial analogue. Full article
(This article belongs to the Special Issue Research in Special Functions)
19 pages, 324 KiB  
Article
Binomial Series Involving Harmonic-like Numbers
by Chunli Li and Wenchang Chu
Axioms 2024, 13(3), 162; https://doi.org/10.3390/axioms13030162 - 29 Feb 2024
Cited by 1 | Viewed by 1089
Abstract
By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in terms of the Riemann and Hurwitz zeta functions as well as logarithm and polylogarithm functions will be established, [...] Read more.
By computing definite integrals, we shall examine binomial series of convergence rate ±1/2 and weighted by harmonic-like numbers. Several closed formulae in terms of the Riemann and Hurwitz zeta functions as well as logarithm and polylogarithm functions will be established, including a conjectured one made recently by Z.-W. Sun. Full article
(This article belongs to the Special Issue Research in Special Functions)
17 pages, 410 KiB  
Article
A New Family of Appell-Type Changhee Polynomials with Geometric Applications
by Rashad A. Al-Jawfi, Abdulghani Muhyi and Wadia Faid Hassan Al-shameri
Axioms 2024, 13(2), 93; https://doi.org/10.3390/axioms13020093 - 30 Jan 2024
Viewed by 1141
Abstract
Recently, Appell-type polynomials have been investigated and applied in several ways. In this paper, we consider a new extension of Appell-type Changhee polynomials. We introduce two-variable generalized Appell-type λ-Changhee polynomials (2VGATλCHP). The generating function, series representations, and summation identities related [...] Read more.
Recently, Appell-type polynomials have been investigated and applied in several ways. In this paper, we consider a new extension of Appell-type Changhee polynomials. We introduce two-variable generalized Appell-type λ-Changhee polynomials (2VGATλCHP). The generating function, series representations, and summation identities related to these polynomials are explored. Further, certain symmetry identities involving two-variable generalized Appell-type λ-Changhee polynomials are established. Finally, Mathematica was used to examine the zero distributions of two-variable truncated-exponential Appell-type Changhee polynomials. Full article
(This article belongs to the Special Issue Research in Special Functions)
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17 pages, 383 KiB  
Article
Matrix Approaches for Gould–Hopper–Laguerre–Sheffer Matrix Polynomial Identities
by Tabinda Nahid, Parvez Alam and Junesang Choi
Axioms 2023, 12(7), 621; https://doi.org/10.3390/axioms12070621 - 21 Jun 2023
Cited by 3 | Viewed by 832
Abstract
The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques. By leveraging properties of Pascal functionals and Wronskian matrices, we derive several identities for these polynomials, including recurrence relations. It is highlighted that [...] Read more.
The Gould–Hopper–Laguerre–Sheffer matrix polynomials were initially studied using operational methods, but in this paper, we investigate them using matrix techniques. By leveraging properties of Pascal functionals and Wronskian matrices, we derive several identities for these polynomials, including recurrence relations. It is highlighted that these identities, acquired via matrix techniques, are distinct from the ones obtained when using operational methods. Full article
(This article belongs to the Special Issue Research in Special Functions)
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