Related papers: Truncated Euler polynomials
We consider the relation between Euler's trinomial problem and the problem of decomposition of tensor powers of adjoint representation of $A_1$ Lie algebra. By using this approach, some new results for both problems are obtained.
In this paper we introduce a new concept of key polynomials for a given valuation $\nu$ on $K[x]$. We prove that such polynomials have many of the expected properties of key polynomials as those defined by MacLane and Vaqui\'e, for…
We give a formula for the Euler characteristic of a triangulated manifold of even dimension in terms of the numbers of even-dimensional faces only. The coefficients in this formula are universal (they do not depend on the dimension of the…
The $(q,r)$-Eulerian polynomials are the $(\maj-$$\exc,\fix,\exc)$ enumerative polynomials of permutations. Using Shareshian and Wachs' exponential generating function of these Eulerian polynomials, Chung and Graham proved two symmetrical…
In this paper we establish the relation between key polynomials (as defined in \cite{SopivNova}) and minimal pairs of definition of a valuation. We also discuss truncations of valuations on a polynomial ring $K[x]$. We prove that a…
Define a ``truncation'' $r_{t}(p)$ of a polynomial $p$ in $\{x_1,x_2,x_3,...\}$ as the polynomial with all but the first $t$ variables set to zero. In certain good cases, the truncation of a Schubert or Grothendieck polynomial may again be…
In this paper, we mainly show that Euler sums of generalized hyperharmonic numbers can be expressed in terms of linear combinations of the classical Euler sums.
In \cite{luo2006,luosri2005}, Luo and Srivastava introduced some generalizations of the Apostol -Bernoulli polynomials and the Apostol-Euler polynomials. The main object of this paper is to extend the result of \cite{prevost2010} to these…
We derive several symmetric identities for Bernoulli and Euler polynomials which imply some known identities. Our proofs depend on the new technique developed in part I and some identities obtained in [European J. Combin. 24(2003),…
In this paper, by using some families of special numbers and polynomials with their generating functions, we give various properties of these numbers and polynomials. These numbers are related to the well-known numbers and polynomials,…
The notion of the truncated Euler characteristic for Iwasawa modules is a generalization of the the usual Euler characteristic to the case when the cohomology groups are not finite. Let $p$ be an odd prime, $E_1$ and $E_2$ be elliptic…
In this paper, we consider the degenerate Frobenius-Euler polynomials and investigate some identities of these polynomials.
We study consistent truncations in the framework of Exceptional Generalised Geometry. We classify the 4-dimensional gauged supergravities that can be obtained as a consistent truncation of 10/11-dimensional supergravity. Any truncation is…
This paper introduces a colored generalization of the Eulerian polynomials, denoted the $\alpha$-colored Eulerian polynomials. We first compute these polynomials by taking the $h$-vector of the $\alpha$-colored permutohedron, a colored…
This paper has two primary contributions. First, we explore degenerate Sheffer-type polynomials, a hybrid of higher-order degenerate Bernoulli and Euler polynomials, and derive their properties. Second, assuming that the moment generating…
This paper is a study of power series, where the coefficients are binomial expressions (iterated finite differences). Our results can be used for series summation, for series transformation, or for asymptotic expansions involving Stirling…
We study the umbral "classical" orthogonal polynomials with respect to a generalized derivative operator $\cal D$ which acts on monomials as ${\cal D} x^n = \mu_n x^{n-1}$ with some coefficients $\mu_n$. Let $P_n(x)$ be a set of orthogonal…
For $m$ an even positive integer and $p$ a prime, we show that the generalized Euler polynomial $E_{mp}^{(mp)}(x)$ is in Eisenstein form with respect to $p$ if and only if $p$ does not divide $m (2^m-1)B_m$. As a consequence, we deduce that…
We give a determination of the equivalence group of Euler-Bernoulli equation and of one of its generalizations, and thus derive some symmetry properties of this equation.
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.…