Related papers: Symmetry identities for 2-variable Apostol type an…
Some properties and relations satisfied by the polynomial solutions of the bispectral problem are studied. Given a differential operator, under certain restrictions its polynomial eigenfunctions are explicitly obtained, as well as the…
We present several identities with a form of polynomials or rational functions that involve Pochhammer and q-Pochhammer symbols and q-binomials (i.e. Gauss polynomials). All these identities were obtained by some analytical methods based on…
In this paper, we give some identities of symmetry for the generalized degenerate Euler polynomials attached to chi which are derived from the symmetric properties for certain fermionic p-adic integrals on Zp.
In this paper we construct the main algebraic and differential properties and the weight functions of orthogonal polynomial solutions of bivariate second--order linear partial differential equations, which are admissible potentially…
We present an informal review of results on asymptotics of orthogonal polynomials, stressing their spectral aspects and similarity in two cases considered. They are polynomials orthonormal on a finite union of disjoint intervals with…
The aim of this paper is to investigate some properties, recurrence relations and identities involving degenerate Stirling numbers of both kinds associated with degenerate hyperharmonic numbers and also with degenerate Bernolli, degenerate…
We prove that uniform hyperbolicity is invariant under topological conjugacy for dissipative polynomial automorphisms of C^2. Along the way we also show that a sufficient condition for hyperbolicity is that local stable and unstable…
A product difference equation is proved and used for derivation by elementary methods of four combinatorial identities, eight combinatorial identities involving generalized harmonic numbers and eight combinatorial identities involving…
The 2-adic valuation of the Stirling numbres is examined. We conjecture pattrens about the distributions of these valuations in residue classes modulo powers of 2.
Let $A$ and $B$ be finite-dimensional simple algebras with arbitrary signature over an algebraically closed field. Suppose $A$ and $B$ are graded by a semigroup $S$ so that the graded identitical relations of $A$ are the same as those of…
We prove two polynomial identities which are particular cases of a conjecture arising in the theory of L-functions of twisted Carlitz modules. This conjecture is stated in earlier papers of the second author.
We develop a method to construct algebraic invariants for hypermatrices. We then construct hyperdeterminants and exhibit a generalization of the Cayley-Hamilton theorem for hypermatrices.
The space of polynomials in two real variables with values in a 2-dimensional irreducible module of a dihedral group is studied as a standard module for Dunkl operators. The one-parameter case is considered (omitting the two-parameter case…
In recent years, studying degenerate versions of various special polynomials and numbers have attracted many mathematicians. Here we introduce degenerate type 2 Bernoulli polynomials, fully degenerate type 2 Bernoulli polynomials and…
The goal of this paper is to present a Dunkl-Gamma type operator with the help of two-variable Hermite polynomials and to derive its approximating properties via the classical modulus of continuity, second modulus of continuity and Peetre's…
In the paper, the author elementarily unifies and generalizes eight identities involving the functions $\frac{\pm1}{e^{\pm t}-1}$ and their derivatives. By one of these identities, the author establishes two explicit formulae for computing…
The generic monic polynomial of sixth degree features 6 a priori arbitrary coefficients. We show that if these 6 coefficients are appropriately defined in two different ways|in terms of 5 arbitrary parameters, then the 6 roots of the…
We perform certain alternating binomial summations with parameters that occur in the analysis of algorithms. A combination of integral and special function and special number representations is used. The results are sufficiently general to…
The aim of this paper is twofold. The first one is to find several relations between the type 2 higher-order degenerate Euler polynomials and the type 2 higher-order Changhee polynomials in connection with the degenerate stirling numbers of…
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