Related papers: The formula of Melzak for arbitrary polynomials

We extend Carleson's formula to radially polynomially weighted Dirichlet spaces.

We study a natural analogue of Collatz's Conjecture for polynomials over $\mathbb{F}_2$.

We prove a series of Stephan's conjectures concerning Pascal triangle modulo 2 and give a polynomial generalization.

We prove a duality formula for certain sums of values of poly-Bernoulli polynomials which generalizes dualities for poly-Bernoulli numbers. We first compute two types of generating functions for these sums, from which the duality formula is…

The main purpose and motivation of this article is to create a linear transformation on the polynomial ring of rational numbers. A matrix representation of this linear transformation based on standard fundamentals will be given. For some…

In this paper we will give a proof of a certain summation formula for Gamma functions utilizing Gegenbauer polynomials.

For functions defined on C^n or (R_+)^n we construct a dequantization transform, which is closely related to the Maslov dequantization. The subdifferential at the origin of a dequantized polynomial coincides with its Newton polytope. For…

In this paper, we introduce a certain method to construct polynomials producing many absolute pseudoprimes. By this method, we give new polynomials producing absolute pseudoprimes with any fixed number of prime factors which can be viewed…

In this paper one extends the binomial and trinomial coefficients to the concept of 'k-nomial' coefficients, and one obtains some properties of these. As an application one generalizes Pascal's triangle.

We study conditions determining the $L^p$ boundedness of multiple Hilbert transforms associated with polynomials.

Partial ordinary Bell polynomials are used to formulate and prove a version of the Fa\`{a} di Bruno's formula which is convenient for handling nonlinear terms in the differential transformation. Applicability of the result is shown in two…

In this article, we give a formula for the generalization of the binomial coefficient to the complex numbers as a linear combination of $\sinc$ functions. We then give a general formula to compute the integral on the real line of the…

We consider here a particular quadratic equation linking two elements of a C-Algebra. By analysing powers of the unknowns, it appears a double sequence of polynomials related to classical Bernoulli polynomials. We get the generating…

We prove a version of van der Corput's Lemma for polynomials over the p-adic numbers.

We prove a formula for double Schubert and Grothendieck polynomials specialized to two rearrangements of the same set of variables. Our formula generalizes the usual formulas for Schubert and Grothendieck polynomials in terms of RC-graphs,…

Second-order polynomials generalize classical first-order ones in allowing for additional variables that range over functions rather than values. We are motivated by their applications in higher-order computational complexity theory,…

In this article we present a generalization of a Leibniz's geometrical theorem and an application of it.

We extend the Ax-Katz theorem for a single polynomial from finite fields to the rings Z_m with m composite. This extension not only yields the analogous result, but gives significantly higher divisibility bounds. We conjecture what computer…

We prove an important property of the binomial transform: it converts multiplication by the discrete variable into a certain difference operator. We also consider the case of dividing by the discrete variable. The properties presented here…

We present new classes of permutation polynomials over finite fields.