Dedicated to the memory of Professor Richard Askey (1933–2019) and to pay tribute to the Bateman Project. Harry Bateman planned his “shoe-boxes” project (accomplished after his death as Higher Transcendental Functions, Vols. 1–3, 1953–1955, under the...
Evaluation of images of special functions under operators of fractional calculus has become a hot topic with hundreds of recently published papers. These are growing daily and we are able to comment here only on a few of them, including also some of...
We introduce a modern methodology for constructing global analytical approximations of special functions over their entire domains. By integrating the traditional method of matching asymptotic expansions—enhanced with Padé approximants&m...
In recent years, our research on biomechanical and biophysical problems has involved a series of symmetry issues. We found that the fundamental laws of the aforementioned problems can all be characterized by fractal operators, and each type of operat...
We show that Lie groups and their respective algebras, special functions and rigged Hilbert spaces are complementary concepts that coexist together in a common framework and that they are aspects of the same mathematical reality. Special functions se...
In the survey Kiryakova: “A Guide to Special Functions in Fractional Calculus” (published in this same journal in 2021) we proposed an overview of this huge class of special functions, including the Fox H-functions, the Fox–Wright g...
The Riemann-Liuoville fractional integrals are the simplest and most popular operators of the classical fractional calculus. But their variants, the Erdélyi-Kober operators of fractional integration, have many more applications due to the free...
Here, we study the extension of p-trigonometric functions sinp and cosp family in complex domains and p-hyperbolic functions sinhp and the coshp family in hyperbolic complex domains. These functions satisfy analogous relations as their classical coun...
Lagrangian formalism is established for differential equations with special functions of mathematical physics as solutions. Formalism is based on either standard or non-standard Lagrangians. This work shows that the procedure of deriving the standard...
In this work, the geometric nature of solutions to two second-order differential equations, zy′′(z)+a(z)y′(z)+b(z)y(z)=0 and z2y′′(z)+a(z)y′(z)+b(z)y(z)=d(z), is studied. Here, a(z), b(z), and d(z) are analytic fun...
A Deviation from competitive neutrality is one of the main problems faced by Chinese state-owned enterprises. Based on the orientation of the classification reform of state-owned enterprises to all kinds of enterprises, we discuss the competitive neu...
Background/Objectives: The relationship between executive functions, special educational needs (SEN), and learning difficulties in school-aged children is critical for developing effective educational interventions. This study explores the connection...
Against the backdrop of urban–rural integrated development, special ecological function zones, as spatial carriers with significant regional ecological value and rural development functions, are confronted with a striking conflict between ecolo...
In this paper, the authors analyse and study some recent publications about integral inequalities related to generalized convex functions of several variables and the use of extended fractional integrals. In particular, they establish a new Hermite&n...
In this article, we use the applications of special functions in the form of Chebyshev polynomials to find the approximate solution of hyperbolic partial differential equations (PDEs) arising in the mathematical modeling of transmission line subject...
We supplement the formulas for partial sums of the Hurwitz zeta-function and its derivatives, producing more integral representations and generic definitions of important constants. Then, these are used, coupled with the functional equation for the c...
The aim of this paper is to derive formulae for the generating functions of the Bernstein type polynomials. We give a PDE equation for this generating function. By using this equation, we give recurrence relations for the Bernstein polynomials. Using...
In this paper, a new approach to find exact solutions is carried out for a generalized unsteady magnetohydrodynamic transport of a rate-type fluid near an unbounded upright plate, which is analyzed for ramped-wall temperature and velocity with consta...
This Special Issue contains 14 articles from the MDPI journal Symmetry on the general subject area of “Special Functions and Polynomials”, written by scholars belonging to different countries of the world. A similar number of submitted ar...
The plant specialized metabolome consists of a multitude of structurally and functionally diverse metabolites, variable from species to species. The specialized metabolites play roles in the response to environmental changes and abiotic or biotic str...
22 November 2022
In this study we focus on the application of standardized tests aimed at evaluating the functional degree of independence in children (client 1, WeeFIM test; and client 2, FIM test) in special education diagnostics. The target group consisted of two...
In this paper, we aim to construct inequalities of the Redheffer type for certain functions defined by the infinite product involving the zeroes of these functions. The key tools used in our proofs are classical results on the monotonicity of the rat...
Current findings of neighboring genes involved in plant specialized metabolism provide the genomic signatures of metabolic evolution. Two such genomic features, namely, (i) metabolic gene cluster and (ii) neo-functionalization of tandem gene duplicat...
Due to their remarkable properties, a plethora of special functions have been crafted and harnessed across a diverse spectrum of fields spanning centuries [...]
Specialized products can be needed to help meet the nutrition requirements of vulnerable populations, including infants and young children, those who are ill, and older adults. Laws and regulations delineate distinct categories for such products incl...
A novel chaotic system for generating multi-scroll attractors based on a Jerk circuit using a special form of a sine function (SFSF) is proposed in this paper, and the SFSF is the product of a sine function and a sign function. Although there are inf...
The aim of this paper is to establish a theorem associated with the product of the Aleph-function, the multivariable Aleph-function, and the general class of polynomials. The results of this theorem are unified in nature and provide a very large numb...
It is indeed a fairly common practice for scientific research journals and scientific research periodicals to publish special issues as well as conference proceedings. Quite frequently, these special issues are devoted exclusively to specific topics...
Rice (Oryza sativa L.) is thought to have been domesticated many times independently in China and India, and many modern cultivars are available. All rice tissues are rich in specialized metabolites (SPMs). To date, a total of 181 terpenoids, 199 phe...
In this paper, we consider a theory of elements u of a groupoid ( X , ∗ ) that are associated with certain functions u ^ : X → X , pseudo-inverse functions, which are generalizations of the inverses associated with units...
This editorial text is a short introductory guide to the book edition of the Special Issue “Analytical and Computational Methods in Differential Equations, Special Functions, Transmutations and Integral Transforms”, which was published in...
This article is devoted to the derivation of the Laplace transforms of the derivatives with respect to parameters of certain special functions, namely, the Mittag–Leffler-type, Wright, and Le Roy-type functions. These formulas show the intercon...
Let p,q≥1 be two real numbers such that 1p+1q=1, and let a,b∈R be two parameters defined on the domain of a function, for example, f. Based on the well known Hölder inequality, we propose a generic inequality of the form |f(ap+bq)|≤|f...
The paper deals with the problem of representing special functions by branched continued fractions, particularly multidimensional A- and J-fractions with independent variables, which are generalizations of associated continued fractions and Jacobi co...
In this paper, we establish new hypergeometric representations for two classical integer sequences, namely the Pell and Jacobsthal sequences. Motivated by Dilcher’s hypergeometric formulations of the Fibonacci sequence, we extend this framework...
While browsing through the famous book of Bierens de Haan, we came across a table with some very interesting integrals. These integrals also appeared in the book of Gradshteyn and Ryzhik. Derivation of these integrals are not listed in the current li...
In the current work, we introduce a special family of the function family of analytic and m-fold symmetric bi-univalent functions and obtain estimates of the Taylor–Maclaurin coefficients |dm+1| and |d2m+1| for functions in the special family....
The manuscript surveys the special functions of the Fox-Wright type. These functions are generalizations of the hypergeometric functions. Notable representatives of the type are the Mittag-Leffler functions and the Wright function. The integral repre...
In this paper, we introduce a special family Mσm(τ,ν,η,φ) of the function family σm of m-fold symmetric bi-univalent functions defined in the open unit disc D and obtain estimates of the first two Taylor–Maclaurin coe...
While rhizosphere microbiome functions in saline soils are well documented, complementary microbial strategies between pioneer and late-successional halophytes remain unexplored. Here, we used 16S rRNA sequencing and FAPROTAX functional prediction to...
In this paper, we first discuss the convolution series that are generated by Sonine kernels from a class of functions continuous on a real positive semi-axis that have an integrable singularity of power function type at point zero. These convolution...
In this Special Issue, the recent advances in the applications of symmetric functions for mathematics and mathematical physics are reviewed, including many novel techniques in analytic functions, transformation methods, economic growth models, and Hu...
The purpose of this article is to give relations among the uniform B-splines, the Bernstein basis functions, and certain families of special numbers and polynomials with the aid of the generating functions method. We derive a relation between generat...
This paper presents a method for parameterizing new Lorentz spacetime coordinates based on coupled parameters. The role of symmetry in rapidity in special relativity is explored, and invariance is obtained for new spacetime intervals with respect to...
In this paper, we propose some generalized integral inequalities of the Raina type depicting the Mittag–Leffler function. We introduce and explore the idea of generalized s-type convex function of Raina type. Based on this, we discuss its algebraic p...
The derivation of integrals in the table of Gradshteyn and Ryzhik in terms of closed form solutions is always of interest. We evaluate several of these definite integrals of the form ∫ 0 ∞ log ( 1 ± e − α y )...
In this paper, we consider and study in detail the generalized Fox–Wright function Ψ˜qp introduced in our recent work as an extension of the Fox–Wright function Ψqp. This special function can be seen as an important case of...
The symmetric Schur process has many different types of formals, such as the functional differential, functional integral, and special functional processes based on special functions. In this effort, the normalized symmetric Schur process (NSSP) is d...
This article introduces certain algebraic properties of generalized (h˜1,h˜2)-pre-invex functions on Rℵ(0<ℵ≤1). A new fractal weighted integral identity is established and further employed to obtain several Ostrowski...
The aim of this paper is to derive some new generalized fractional analogues of Mercer type inequalities, essentially using the convexity property of the functions and Raina’s function. We also discuss several new special cases which show that...
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