Related papers: A new approach to Bell and poly-Bell numbers and p…
In this paper, we reveal an internal structure within Dedekind numbers, demonstrating that they can be expressed as polynomials of powers of 2. This discovery is based on innovative concepts and methods, offering a new perspective on the…
Dowling showed that the Whitney numbers of the first kind and of the second kind satisfy Stirling number-like relations. Recently, Kim-Kim introduced the degenerate r-Whitney numbers of the first kind and of the second kind, as degenerate…
In the recent paper the interesting q-Euler numbers and polynomials introduced in JMAA. The purpose of this paper is to construct the modified q-Euler numbers and polynomiasl. Finally we will give the interesting many identities related to…
In the paper, the author finds an explicit formula for computing Bell numbers in terms of Lah numbers and Stirling numbers of the second kind.
Recursive formulas are derived for the number of solutions of linear and quadratic Diophantine equations with positive coefficients. This result is further extended to general non-linear additive Diophantine equations. It is shown that all…
This article aims to reinforce the broad applicability of the umbral approach to address complex mathematical challenges and contribute to various scientific and engineering endeavors. The umbral methods are used to reformulate the…
In this paper, we study some combinations of the degenerate and incomplete Stirling numbers of the second kind. We use a combinatorial approach and provide some asymptotic results.
This paper is devoted to establishing several new formulas relating Bernoulli and Stirling numbers of both kinds.
We introduce the generalized degenerate Euler-Genocchi polynomials as a degenerate version of the Euler-Genocchi polynomials. In addition, we introduce their higher-order version, namely the generalized degenerate Euler-Genocchi polynomials…
Recently, Komatsu introduced the concept of poly-Cauchy numbers and polynomials which generalize Cauchy numbers and polynomials. In this paper, we consider the new concept of higher-order Cauchy numbers and polynomials which generalize…
We derive new matrix representation for higher order Daehee numbers and polynomials, the higher order lambda-Daehee numbers and polynomials and the twisted lambda-Daehee numbers and polynomials of order k. This helps us to obtain simple and…
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,…
In this paper we focus on two new families of polynomials which are connected with exponential polynomials and geometric polynomials. We discuss their generalizations and show that these new families of polynomials and their generalizations…
In this paper, we consider the q-extensions of Boole polynomials. From those polynomials, we derive some new and interesting properties and identities related to special polynomials.
Recently, Masjed-Jamei-Beyki-Koepf studied the so called new type Euler polynomials without making use of Euler polynomials of complex variable. Here we study degenerate and type 2 versions of these new type Euler polynomials, namely the…
Recently, Daehee numbers and polynomials are introduced by the authors. In this paper, we consider the Daehee numbers and polynomials of order k and give some relation between Daehee polynomials of order k and special polynomials
We introduce a family of sequence transformations, defined via partial Bell polynomials, that may be used for a systematic study of a wide variety of problems in enumerative combinatorics. This family includes some of the transformations…
In this paper special values of Bell polynomials are given by using the power series solution of the equation $y^{(k)}=e^{ay}$. In addition, complete and partial exponential autonomous functions, exponential autonomous polynomials,…
The differential transform method is used to find numerical approximation of solution to a class of certain nonlinear differential algebraic equations. The method is based on Taylor's theorem. Coefficients of the Taylor series are…
In this paper, we introduce poly-Bernoulli numbers with level $2$, related to the Stirling numbers of the second kind with level $2$, and study several properties of poly-Bernoulli numbers with level $2$ from their expressions, relations,…