Special Issue "Trend Topics in Special Functions and Polynomials: Theory, Methods, Applications and Modeling"

Submission Deadline: 31 December 2021
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Guest Editors
Dr. Serkan Araci, Hasan Kalyoncu University, Turkey
Prof. Dr. Juan Luis García Guirao, Universidad Politécnica de Cartagena, Spain


The computers began to appear in the 1950s, and often incorrect, estimations were done related to the impact of these devices on applied mathematics, science and engineering. One of these estimations was that the need for special functions, or higher transcendental functions (as they are also known), would disappear entirely. This was based on the observation that the key use of these functions in those days was to approximate the solutions of classical differential (or partial differential) equations: with the mathematical software it would become possible to solve these equations by direct numerical methods. This observation is in fact correct; even so, a study of current computational journals in the sciences reveals a continuous need for numerical algorithms to generate Airy functions, Bessel functions, Coulomb wave functions, error functions and exponential integrals, etc.

This special issue focuses on the applications and computer modeling of the special functions and polynomials to various areas of mathematics. Thorough knowledge of special functions is required in modern engineering, physical science applications and computer modeling. These functions typically arise in such applications as communications systems, statistical probability distribution, electro-optics, nonlinear wave propagation, electromagnetic theory, potential theory, electric circuit theory, and quantum mechanics.

Potential topics include but are not limited to the following:

 Computer modeling of Special functions and polynomials

 Analytical properties and applications of Special functions.

 Inequalities for Special Functions

 Integration of  products of Special Functions

 Properties of ordinary and general families of Special Polynomials

 Operational techniques involving Special Polynomials

 Classes of mixed Special Polynomials and their properties

 Other miscellaneous applications of Special Functions and Special Polynomials

Hypergeometric functions and their extensions; Generalized functions and their extensions; Generalized inequalities and their extensions; Operational techniques; Mixed special polynomials; Applications; Computer modeling.

Published Papers

  • Study of Degenerate Poly-Bernoulli Polynomials by λ-Umbral Calculus
  • Abstract Recently, degenerate poly-Bernoulli polynomials are defined in terms of degenerate polyexponential functions by Kim-Kim-Kwon-Lee. The aim of this paper is to further examine some properties of the degenerate poly-Bernoulli polynomials by using three formulas from the recently developed ‘λ-umbral calculus.’ In more detail, we represent the degenerate poly-Bernoulli polynomials by Carlitz Bernoulli polynomials and degenerate Stirling numbers of the first kind, by fully degenerate Bell polynomials and degenerate Stirling numbers of the first kind, and by higherorder degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind. More
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