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Relations have been derived which establish connection between a scalar or a vector functions and the integral of Laplace operator of these functions (the integral property of Laplace operator). The integral property of Laplace operator was…
We introduce the fractal expansions, sequences of integers associated to a number. We show that these sequences characterize the O-sequences and encode some information on lex segment ideals. Moreover, we introduce a numerical functions…
The novel concept of box spline of complex degree is introduced and several of its properties derived and discussed. These box splines of complex degree generalize and extend the classical box splines. Relations to a class of fractional…
Previouly a possible extension of the complex number, together with its connected trigonometry was introduced. In this paper we focuss on the simplest case of ternary complex numbers. Then, some types of holomorphicity adapted to the…
We outline here a simple mathematical introduction to the notions of multipoles for a general extensive property $\Pi$ from the point of view of continuum mechanics. Classically, $\Pi$ is the electric charge, but the theory is not limited…
We consider multiple orthogonal polynomials corresponding to two Macdonald functions (modified Bessel functions of the second kind), with emphasis on the polynomials on the diagonal of the Hermite-Pad\'e table. We give some properties of…
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…
One of the main purposes of this article is to give functional equations and differential equations between Bernstein basis functions and generating functions of B-spline curves. Using these equations, very useful formulas containing the…
In this research, the Bernoulli polynomials are introduced. The properties of these polynomials are employed to construct the operational matrices of integration together with the derivative and product. These properties are then utilized…
In many articles on the integral expressions of Mittag-Leffler functions, we have found that whether the integral expression can be used at the origin is still unresolved. In this article we give the applicable conditions and proof. And we…
Properties of the magnetic translation operators for a charged particle moving in a crystalline potential and a uniform magnetic field show that it is necessary to consider all inequivalent irreducible projective representations of the the…
This paper provides a view of Maxwell's equations from the perspective of complex variables. The study is made through complex differential forms and the Hodge star operator in $\mathbb{C}^2$ with respect to the Euclidean and the Minkowski…
Using a deformed calculus based on the Dunkl operator, two new deformations of Bessel functions are proposed. Some properties i.e. generating function, differential-difference equation, recursive relations, Poisson formula... are also given…
We use the properties of Hermite and Kamp\'e de F\'eriet polynomials to get closed forms for the repeated derivatives of functions whose argument is a quadratic or higher-order polynomial. The results we obtain are extended to product of…
In the first part of this paper, we express the generalized Bessel function associated with dihedral systems and a constant multiplicity function as a infinite series of confluent Horn functions. The key ingredient leading to this…
We give some theoretical as well as computational results on Laplace and Maxwell constants. Besides the classical de Rham complex we investigate the complex of elasticity and the complex related to the biharmonic equation and general…
Finite Cartesian products of operators play a central role in monotone operator theory and its applications. Extending such products to arbitrary families of operators acting on different Hilbert spaces is an open problem, which we address…
Properties of the recently reported homogeneous Hilbert curves are deduced and reported. The nature of the affine transformations involved in the construction of the Hilbert curves is explored. The analytical representation of proper and…
We obtain integral representations of the $n$-th derivatives of the Bessel functions with respect to the order. The numerical evaluation of these expressions is very efficient using a double exponential integration strategy. Also, from the…
The present work proposes analytical solutions for the integral of bivariate Fox H-function in combination with algebraic, exponential, and complementary error functions. In addition, the work also presents the derivative identities with…