Related papers: The formula of Melzak for arbitrary polynomials
We prove a binomial formula for Macdonald polynomials and consider applications of it.
In this note we prove an explicit binomial formula for Jack polynomials and discuss some applications of it.
In a rather straightforward manner, we develop the well-known formula for the Stirling numbers of the first kind in terms of the (exponential) complete Bell polynomials where the arguments include the generalised harmonic numbers. We also…
We prove a generalization of classical Montel's theorem for the mixed differences case, for polynomials and exponential polynomial functions, in commutative setting.
We give an explicit formula for the Hankel transform of a regular sequence in terms of the coefficients of the associated orthogonal polynomials and the sequence itself. We apply this formula to some sequences of combinatorial interest,…
We survey various classical results on invariants of polynomials, or equivalently, of binary forms, focussing on explicit calculations for invariants of polynomials of degrees 2, 3, 4.
We extend the authors' previous work on Wiener-Wintner double recurrence theorem to the case of polynomials.
Permutation polynomials are an interesting subject of mathematics and have applications in other areas of mathematics and engineering. In this paper, we develop general theorems on permutation polynomials over finite fields. As a…
We study the generalization of shifted Jack polynomials to arbitrary multiplicity free spaces. In a previous paper (math.RT/0006004) we showed that these polynomials are eigenfunctions for commuting difference operators. Our central result…
In this paper we introduce the generalization of Multi Poly-Euler polynomials and we investigate some relationship involving Multi Poly-Euler polynomials. Obtaining a closed formula for generalization of Multi Poly-Euler numbers therefore…
We fully classify completely multiplicative sequences which are given by generalised polynomial formulae, and obtain a similar result for (not necessarily completely) multiplicative sequences under the additional restriction that the…
A generalization of the classical Leibniz rule for the covariant derivative on a vector bundle is obtained.
We derive inversion formulas involving orthogonal polynomials which can be used to find coefficients of differential equations satisfied by certain generalizations of the classical orthogonal polynomials. As an example we consider special…
We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic…
We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.
Here the polynomial interpolation approach is used to introduce the main results on multivariate normal algebraic systems. Next we bring a construction which shows that any standard algebraic system, with finite set of solutions, can be…
We propose several techniques to construct complete permutation polynomials of finite fields by virtue of complete permutations of subfields. In some special cases, any complete permutation polynomials over a finite field can be used to…
In this paper we present a special formula for transforming integrals to series. The resulting series involves binomial transforms with the Taylor coefficients of the integrand. Five applications are provided for evaluating challenging…
We give a formula and an estimation for the number of irreducible polynomials in two (or more) variables over a finite field.
In the present article, we study Bell based Euler polynomial of order {\alpha} and investigate some useful correlation formula, summation formula and derivative formula. Also, we introduce some relation of string number of the second kind.…