Related papers: Degenerate Euler- Seidel Method for degenerate Ber…
The partial-dual Euler-genus polynomial was defined by Gross, Mansour, and Tucker to analyze how the Euler genus of a ribbon graph changes under partial duality, a generalization of Euler-Poincar\'{e} duality introduced by Chmutov. The…
The aim of this paper is to give a new approach to modified $q$-Bernstein polynomials for functions of several variables. By using these polynomials, the recurrence formulas and some new interesting identities related to the second Stirling…
In the article we develop Euler-Lagrange method and calculate all the roots of an arbitrary complex polynomial $P(z)$ on the base of calculation (similar to the Bernoulli-Aitken-Nikiporets methods) of the limits of ratios of Hadamard…
The purpose of this paper is to present a systemic study of some families of multiple q-Genocchi and euler numbers by using multivariate q-Volkenborn integral. From the studies of those q-Genocchi numbers and polynomials of higher order we…
We investigate a recursively generated sequence of random variables that begins with an Exponential random variable with parameter (i.e., inverse-mean) 1, and continues with additional Exponentials, each of whose random parameter possesses…
The main purpose of this paper is to introduce and investigate a class of $q$-Bernoulli, $q$-Euler and $q$-Genocchi polynomials. The $q$-analogues of well-known formulas are derived. The $q$-analogue of the Srivastava--Pint\'er addition…
We prove that Euler supercharacters for orthosymplectic Lie superalgebras can be obtained as a certain specialization of super Jacobi polynomials. A new version of Weyl type formula for super Schur functions and specialized super Jacobi…
The method of parameter variation for linear differential equations is extended to classes of second order nonlinear differential equations. This allows to reduce the latter to first order differential equations. Known classical equations…
The aim of this paper is to investigate and introduce some new identities related to the unification and generalization of the three families of generalized Apostol type polynomials, which are Apostol-Bernoulli, Apostol-Euler, and…
In this article, a new approach based on linear algebra is adopted to study a hybrid Sheffer polynomial sequences. The recurrence relations and differential equation for these polynomials are derived by using the properties and…
This paper presents a new generalization of the Genocchi numbers and the Genocchi theorem. As consequences, we obtain some important families of integer-valued polynomials those are closely related to the Bernoulli polynomials. Denoting by…
Recently, Bovadzhiev studied a power series whose coefficients are binomial expressions and extended some known formulas involving classical special functions and polynomials. The aim of this paper is to adopt his ideas to express several…
Let $\{B_n\}$, $\{B_n(x)\}$ and $\{E_n(x)\}$ be the Bernoulli numbers, Bernoulli polynomials and Euler polynomials, respectively. In this paper we mainly establish formulas for $\sum_{6\mid k-3}\binom nkB_{n-k}(x)$, $\sum_{6\mid k}\binom…
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabilistic Frobenius-Euler polynomials associated with Y and…
By applying p-adic integral on the set of p-adic integers in [27] (Interpolation Functions for New Classes Special Numbers and Polynomials via Applications of p-adic Integrals and Derivative Operator, Montes Taurus J. Pure Appl. Math. 3…
A generalisation of the odd Bernoulli polynomials related to the quantum Euler top is introduced and investigated. This is applied to compute the coefficients of the spectral polynomials for the classical Lam\'e operator.
We use Seiberg--Witten-like relations in the topological recursion framework to obtain virtual Euler characteristics for uni- and multicellular maps for ensembles of classic orthogonal polynomials and for ensembles related to nonorientable…
E30 in the Enestrom index. Translated from the Latin original "De formis radicum aequationum cuiusque ordinis coniectatio" (1733). For an equation of degree n, Euler wants to define a "resolvent equation" of degree n-1 whose roots are…
In this note we augment the poly-Bernoulli family with two new combinatorial objects. We derive formulas for the relatives of the poly-Bernoulli numbers using the appropriate variations of combinatorial interpretations. Our goal is to show…
In the present paper we generalize the Eulerian numbers (also of the second and third orders). The generalization is connected with an autonomous first-order differential equation, solutions of which are used to obtain integral…