相关论文: Fonctions sp\'eciales et polyn\^omes orthogonaux: …
The Wright function, which arises in the theory of the space-time fractional diffusion equation, is an interesting mathematical object which has diverse connections with other special and elementary functions. The Wright function provides a…
The primary goal of this paper is to introduce and investigate generalized incomplete exponential functions with matrix parameters. Integral representation, differential formula, addition formula, multiplication formula, and recurrence…
Orthogonal rational functions (ORF) on the unit circle generalize orthogonal polynomials (poles at infinity) and Laurent polynomials (poles at zero and infinity). In this paper we investigate the properties of and the relation between these…
Partition functions of eigenvalue matrix models possess a number of very different descriptions: as matrix integrals, as solutions to linear and non-linear equations, as tau-functions of integrable hierarchies and as special-geometry…
We study functional clones, which are sets of non-negative pseudo-Boolean functions (functions $\{0,1\}^k\to\mathbb{R}_{\geq 0}$) closed under (essentially) multiplication, summation and limits. Functional clones naturally form a lattice…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…
This work looks at the theory of octonionic slice regular functions through the lens of differential topology. It proves a full-fledged version of the Open Mapping Theorem for octonionic slice regular functions. Moreover, it opens the path…
We consider and provide an accurate study for the fractional Zernike functions on the punctured unit disc, generalizing the classical Zernike polynomials and their associated $\beta$-restricted Zernike functions. Mainly, we give the…
In modern quantum field theory, one of the most important tasks is the calculation of loop integrals. Loop integrals appear when evaluating the Feynman diagrams with one or more loops by integrating over the internal momenta. Even though…
Four families of generalizations of trigonometric functions were recently introduced. In the paper the functions are transformed into four families of orthogonal polynomials depending on two variables. Recurrence relations for construction…
In this paper we talk about the so-called SuperMathematics Functions (SMF), which often constiture the base for generating technical neo-geometrical objects.
Spectral Barron spaces, constituting a specialized class of function spaces that serve as an interdisciplinary bridge between mathematical analysis, partial differential equations (PDEs), and machine learning, are distinguished by the decay…
Symmetries play an critical role in finding analytic solutions to nonlinear differential equations. A symmetry is a mapping of the solutions of the differential equation into the solutions and have been studied extensively for over a…
Electromagnetic theory is central to physics. An undergraduate major in physics typically takes a semester or a year of electromagnetic theory as a junior or senior, and a graduate student in physics typically takes an additional semester…
The long-standing problem of representing the general massive one-loop Feynman integral as a meromorphic function of the space-time dimension $d$ has been solved for the basis of scalar one- to four-point functions with indices one. In 2003…
We introduce one- and two-dimensional `exponential shapelets': orthonormal basis functions that efficiently model isolated features in data. They are built from eigenfunctions of the quantum mechanical hydrogen atom, and inherit mathematics…
In classical physics, the familiar sine and cosine functions appear in two forms: (1) geometrical, in the treatment of vectors such as forces and velocities, and (2) differential, as solutions of oscillation and wave equations. These two…
This document is the manual for a free Mathematica package for computing with harmonic functions. This package allows the user to make calculations that would take a prohibitive amount of time if done without a computer. For example, the…
Properties of four infinite families of special functions of two real variables, based on the compact simple Lie group G2, are compared and described. Two of the four families (called here C- and S-functions) are well known, whereas the…
This article introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under "mathematics" we include also all computer simulations if…