Related papers: Polynomial Form of Binary Cyclotomic Polynomials

A bilinear formulation for the supersymmetric two-boson equation is derived. As applications, some solutions are calculated for it. We also construct a bilinear Backlund transformation.

Spivey presented a new approach to evaluate combinatorial sums by using finite differences. We present some closed forms for sums involving the binomial coefficients, Fibonacci and Lucas numbers in terms of the falling factorial.

A system of biorthogonal polynomials with respect to a complex valued measure supported on the unit circle is considered and all the terms with bounds are explicitly given for the remainder of an asymptotic formula given by R. Askey for…

This is an extended version of our note in the Notices of the American Mathematical Society 63 (2016), no. 9, in which we explain what multiple orthogonal polynomials are and where they appear in various applications.

In this paper, we define multi poly-Bernoulli polynomials using multiple polylogarithm and derive some properties parallel to those of poly-Bernoulli polynomials. Furthermore, an explicit formula for certain Hurwitz-Lerch type multi…

In this paper, we consider central complete and incomplete Bell polynomials which are generalizations of the recently introduced central Bell polynomials and central analogues for the complete and incomplete Bell polynomials. We investigate…

This note provides new closed forms evaluations of a few classes of exponential sums associated with elliptic curves and hyperelliptic curves.

In this paper, we consider the problem of representing any polynomial in terms of the degenerate Bernoulli polynomials and more generally of the higher-order degenerate Bernoulli polynomials. We derive explicit formulas with the help of…

This is a complete classification of the complex forms of quaternionic symmetric spaces

This article is a survey of the exponential polynomials (also called single-variable Bell polynomials) from the point of view of Analysis. Some new properties are included and several Analysis-related applications are mentioned.

In this paper we investigate some interesting formulae of q-Euler numbers and polynomials related to the modified q-Bernstein polynomials.

Cyclotomic polylogarithms are reviewed and new results concerning the special constants that occur are presented. This also allows some comments on previous literature results using PSLQ.

A simple procedure to obtain complete, closed expressions for Lie algebra invariants is presented. The invariants are ultimately polynomials in the group parameters. The construction of finite group elements require the use of projectors,…

Exponential sums have applications to a variety of scientific fields, including, but not limited to, cryptography, coding theory and information theory. Closed formulas for exponential sums of symmetric Boolean functions were found by Cai,…

Comment on the Letter ``Polynomial-Time Simulation of Pairing Models on a Quantum Computer'', L. A. Wu, M. S. Byrd and D. A. Lidar, Phys. Rev. Lett. 89, 057904 (2002).

The derivative polynomials for the hyperbolic and trigonometric tangent, cotangent and secant are found in explicit form, where the coefficients are given in terms of Stirling numbers of the second kind. As application, some integrals are…

We introduce a multivariate analogue of Bernoulli polynomials and give their fundamental properties: difference and differential relations, symmetry, explicit formula, inversion formula, multiplication theorem, and binomial type formula.…

In this article we give a totally new proof of the integral localization formula for equivariantly closed differential forms (Theorem 7.11 in [BGV]). We restate it here as Theorem 2. This localization formula is very well known, but the…

In this paper, we establish a q-analog of partial fraction decomposition formula. By using formula, we develop new closed form representations of sums of q-harmonic numbers and reciprocal q-binomial coefficients. Moreover, we give explicit…

Combinatorial formulas expressing cyclic rook polynomials and cyclic permanents of rectangular matrices in terms of expansions along rows are presented