Search for Articles:
Title / Keyword
Author / Affiliation / Email
Journal
Article Type
 
 
Advanced Search
 
Section
Special Issue
Volume
Issue
Number
Page
 
4.6
2.2
Journals
Mathematics
Special Issues
Special Functions with Applications
mathematics-logo
Submit to Mathematics Review for Mathematics Propose a Special Issue

Journal Menu

► Journal Menu

Journal Browser

► Journal Browser
share announcement

Special Functions with Applications

A special issue of Mathematics (ISSN 2227-7390).

Deadline for manuscript submissions: closed (30 November 2025) | Viewed by 9160

Special Issue Editor

Dr. Vito Lampret

E-Mail Website
Guest Editor
Faculty of Civil and Geodetic Engineering, University of Ljubljana, 1000 Ljubljana, Slovenia
Interests: asymptotic expansion; completely monotonic function; gamma function; elliptic integral; trigonometric function; arithmetic mean

Special Issue Information

Dear Colleagues,

This Special Issue, “Special Functions with Applications”, focuses on the study and utilization of special functions, which are mathematically significant and arise in applied mathematics and various fields of science. These functions, such as Bessel functions, hypergeometric functions, orthogonal polynomials, functions relating to the gamma function, etc., play a crucial role in solving differential equations, integral transforms, and problems in mathematical physics. The aim of this topic is to explore the theoretical foundations, computational methods, and practical applications of special functions, bridging the gap between pure mathematics and real-world problems.

This topic welcomes research on the development of new analytical and numerical techniques for evaluating special functions, as well as their applications in areas such as quantum mechanics, signal processing, fluid dynamics, and statistical mechanics. Contributions may also include interdisciplinary studies that leverage special functions to solve complex problems in engineering, computer science, and beyond. By fostering collaboration between mathematicians, physicists, and engineers, this Special Issue seeks to advance our understanding of special functions and expand their utility in cutting-edge applications.

Dr. Vito Lampret
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

  • special functions
  • Airy function
  • Bessel function
  • Fresnel, Hankel, Kelvin, Lambert, Mathieu, etc., functions
  • hypergeometric functions
  • orthogonal polynomials Functions relating to the gamma function (fractional calculus functions)
  • differential equations
  • integral transforms
  • mathematical physics computational methods
  • quantum mechanics
  • signal processing
  • fluid dynamics
  • statistical mechanics
  • applied mathematics
  • numerical techniques

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.

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

21 pages, 513 KB  
Article
Application of Natural Generalized-Laplace Transform and Its Properties
by Hassan Eltayeb
Mathematics 2025, 13(19), 3194; https://doi.org/10.3390/math13193194 - 5 Oct 2025
Cited by 1 | Viewed by 415
Abstract
In this work, we combine the Natural Transform and generalized-Laplace Transform into a new transform called, the Natural Generalized-Laplace Transform, (NGLT) and some of its properties are provided. Moreover, the existence condition, convolution theorem, periodic theorem, and non-constant coefficient partial derivatives are proved [...] Read more.
In this work, we combine the Natural Transform and generalized-Laplace Transform into a new transform called, the Natural Generalized-Laplace Transform, (NGLT) and some of its properties are provided. Moreover, the existence condition, convolution theorem, periodic theorem, and non-constant coefficient partial derivatives are proved with some details. The (NGLT) is applied to gain the solutions of linear telegraph and partial integro-differential equations. Also, we obtained the solution of the singular one-dimensional Boussinesq equation by employing the Natural Generalized-Laplace Transform Decomposition Method, (NGLTDM). Full article
(This article belongs to the Special Issue Special Functions with Applications)
►▼ Show Figures

Figure 1

10 pages, 231 KB  
Article
Composition of Activation Functions and the Reduction to Finite Domain
by George A. Anastassiou
Mathematics 2025, 13(19), 3177; https://doi.org/10.3390/math13193177 - 3 Oct 2025
Viewed by 1373
Abstract
This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the composition of two general [...] Read more.
This work takes up the task of the determination of the rate of pointwise and uniform convergences to the unit operator of the “normalized cusp neural network operators”. The cusp is a compact support activation function, which is the composition of two general activation functions having as domain the whole real line. These convergences are given via the modulus of continuity of the engaged function or its derivative in the form of Jackson type inequalities. The composition of activation functions aims to more flexible and powerful neural networks, introducing for the first time the reduction in infinite domains to the one domain of compact support. Full article
(This article belongs to the Special Issue Special Functions with Applications)
10 pages, 265 KB  
Article
Horváth Spaces and a Representations of the Fourier Transform and Convolution
by Emilio R. Negrín, Benito J. González and Jeetendrasingh Maan
Mathematics 2025, 13(15), 2435; https://doi.org/10.3390/math13152435 - 28 Jul 2025
Viewed by 511
Abstract
This paper explores the structural representation and Fourier analysis of elements in Horváth distribution spaces Sk′, for k<−n. We prove that any element in Sk′ can be expressed as a finite sum of derivatives [...] Read more.
This paper explores the structural representation and Fourier analysis of elements in Horváth distribution spaces Sk′, for k<−n. We prove that any element in Sk′ can be expressed as a finite sum of derivatives of continuous L1(Rn)-functions acting on Schwartz test functions. This representation leads to an explicit expression for their distributional Fourier transform in terms of classical Fourier transforms. Additionally, we present a distributional representation for the convolution of two such elements, showing that the convolution is well-defined over S. These results deepen our understanding of non-tempered distributions and extend Fourier methods to a broader functional framework. Full article
(This article belongs to the Special Issue Special Functions with Applications)
20 pages, 2586 KB  
Article
An In-Depth Investigation of the Riemann Zeta Function Using Infinite Numbers
by Emmanuel Thalassinakis
Mathematics 2025, 13(9), 1483; https://doi.org/10.3390/math13091483 - 30 Apr 2025
Viewed by 4885
Abstract
This study focuses on an in-depth investigation of the Riemann zeta function. For this purpose, infinite numbers and rotational infinite numbers, which have been introduced in previous studies published by the author, are used. These numbers are a powerful tool for solving problems [...] Read more.
This study focuses on an in-depth investigation of the Riemann zeta function. For this purpose, infinite numbers and rotational infinite numbers, which have been introduced in previous studies published by the author, are used. These numbers are a powerful tool for solving problems involving infinity that are otherwise difficult to solve. Infinite numbers are a superset of complex numbers and can be either complex numbers or some quantification of infinity. The Riemann zeta function can be written as a sum of three rotational infinite numbers, each of which represents infinity. Using these infinite numbers and their properties, a correlation of the non-trivial zeros of the Riemann zeta function with each other is revealed and proven. In addition, an interesting relation between the Euler–Mascheroni constant (γ) and the non-trivial zeros of the Riemann zeta function is proven. Based on this analysis, complex series limits are calculated and important conclusions about the Riemann zeta function are drawn. It turns out that when we have non-trivial zeros of the Riemann zeta function, the corresponding Dirichlet series increases linearly, in contrast to the other cases where this series also includes a fluctuating term. The above theoretical results are fully verified using numerical computations. Furthermore, a new numerical method is presented for calculating the non-trivial zeros of the Riemann zeta function, which lie on the critical line. In summary, by using infinite numbers, aspects of the Riemann zeta function are explored and revealed from a different perspective; additionally, interesting mathematical relationships that are difficult or impossible to solve with other methods are easily analyzed and solved. Full article
(This article belongs to the Special Issue Special Functions with Applications)
►▼ Show Figures

Figure 1

30 pages, 2164 KB  
Article
More Theory About Infinite Numbers and Important Applications
by Emmanuel Thalassinakis
Mathematics 2025, 13(9), 1390; https://doi.org/10.3390/math13091390 - 24 Apr 2025
Cited by 1 | Viewed by 1383
Abstract
In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and [...] Read more.
In the author’s previous studies, new infinite numbers, their properties, and calculations were introduced. These infinite numbers quantify infinity and offer new possibilities for solving complicated problems in mathematics and applied sciences in which infinity appears. The current study presents additional properties and topics regarding infinite numbers, as well as a comparison between infinite numbers. In this way, complex problems with inequalities involving series of numbers, in addition to limits of functions of x ∈ ℝ and improper integrals, can be addressed and solved easily. Furthermore, this study introduces rotational infinite numbers. These are not single numbers but sets of infinite numbers produced as the vectors of ordinary infinite numbers are rotated in the complex plane. Some properties of rotational infinite numbers and their calculations are presented. The rotational infinity unit, its inverse, and its opposite number, as well as the angular velocity of rotational infinite numbers, are defined and illustrated. Based on the above, the Riemann zeta function is equivalently written as the sum of three rotational infinite numbers, and it is further investigated and analyzed from another point of view. Furthermore, this study reveals and proves interesting formulas relating to the Riemann zeta function that can elegantly and simply calculate complicated ratios of infinite series of numbers. Finally, the above theoretical results were verified by a computational numerical simulation, which confirms the correctness of the analytical results. In summary, rotational infinite numbers can be used to easily analyze and solve problems that are difficult or impossible to solve using other methods. Full article
(This article belongs to the Special Issue Special Functions with Applications)
►▼ Show Figures

Figure 1

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