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The functional decomposition of polynomials has been a topic of great interest and importance in pure and computer algebra and their applications. The structure of compositions of (suitably normalized) polynomials f=g(h) over finite fields…
Coxeter polynomials are important homological invariants that are defined for a large class of finite-dimensional algebras. It is of particular interest to develop methods to compute these polynomials. We define the notion of insertion of a…
The authors survey recent results in special functions, particularly the gamma function and the Gaussian hypergeometric function.
Special classes of analytic functions, denoting by K and J arc considered in this paper.
The authors survey recent results in special functions of classical analysis and geometric function theory, in particular the circular and hyperbolic functions, the gamma function, the elliptic integrals, the Gaussian hypergeometric…
An important invariant of a polynomial $f$ is its Jacobian algebra defined by its partial derivatives. Let $f$ be invariant with respect to the action of a finite group of diagonal symmetries $G$. We axiomatically define an orbifold…
Hypercomplex numbers are unital algebras over the real numbers. We offer a short demonstration of the practical value of hypercomplex analytic functions in the field of partial differential equations.
We generalize and complete some of Maxim's recent results on Alexander invariants of a polynomial transversal to the hyperplane at infinity. Roughly speaking, and surprisingly, such a polynomial behaves both topologically and algebraically…
In this paper, we first introduce certain forms of extended incomplete Pochhammer symbols which are then used to define families of extended incomplete generalized hypergeometric functions. For these functions, we investigate various…
In this paper, some geometric properties of inverse polynomial images which consist of a real interval and an arc symmetric with respect to the real line are obtained. The proofs are based on properties of Jacobi's elliptic and theta…
Motivated by the substantial development of the special functions, we contribute to establish some rigorous results on the general series identities with bounded sequences and hypergeometric functions with different arguments, which are…
A certain special function of the generalized hypergeometric variety is shown to fulfill a host of useful noncommutative identities.
We discuss some geometric invariants of polynomial identities of algebras deduced from Kemer's theory and deduce some quantitative information on codimension and co--length
In this paper, we gave some properties of binomial coefficient.
Volume polynomials form a distinguished class of log-concave polynomials with remarkable analytic and combinatorial properties. I will survey realization problems related to them, review fundamental inequalities they satisfy, and discuss…
Some properties and relations satisfied by the polynomial solutions of a bispectral problem are studied. Given a finite order differential operator, under certain restrictions, its polynomial eigenfunctions are explicitly obtained, as well…
Polynomials are common algebraic structures, which are often used to approximate functions including probability distributions. This paper proposes to directly define polynomial distributions in order to describe stochastic properties of…
We introduce a family of extremal polynomials associated with the prolongation of a stratified nilpotent Lie algebra. These polynomials are related to a new algebraic characterization of abnormal subriemannian geodesics in stratified…
This paper is a contribution to the study of the relations between special functions, Lie algebras and rigged Hilbert spaces. The discrete indices and continuous variables of special functions are in correspondence with the representations…
In this paper, we study some properties of associated sequences of special polynomials. From the properties of associated sequences of polynomials, we derive some interesting identities of special polynomials.