arXiv subjects
Publications and source records attributed to Taekyun Kim.
In this paper, we introduce the degenerate central factorial polynomials and numbers of the second kind which are degenerate versions of the central factorial polynomials and numbers of the second kind. We derive some properties and identities for those polynomials and numbers. We obtain, among other things, recursive formulas for the degenerate central factorial polynomials and numbers of the second kind.
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 some properties and identities for these polynomials. Especially, we give explicit formulas for the central complete and incomplete Bell polynomials related to central factorial numbers of the second kind.
In recent years, many authors have studied Changhee and Dae- hee polynomials in connection with many special numbers and polynomials. In this paper, we investigate type 2 Changhee and Daehee numbers and polynomials and give some identities for these numbers and polynomials in relation to type 2 Euler and Bernoulli numbers and polynomials. In addition, we express the central factorial numbers of the second kind in terms of type 2 Bernoulli, type 2 Changhee and type 2 Daehee numbers of negative integral orders.
Here we consider the degenerate Bernstein polynomials as a degenerate version of Bernstein polynomials, which are motivated by Simsek's recent work 'Generating functions for unification of the multidimensional Bernstein polynomials and their applications'([15,16]) and Carlitz's degenerate Bernoulli polynomials. We derived thier generating function, symmetric identities, recurrence relations, and some connections with generalized falling factorial polynomials, higher-order degenerate Bernoulli polynomials and degenerate Stirling numbers of the second kind.
In this paper, we study $λ$-analogues of the r-Stirling numbers of the first kind which have close connections with the r-Stirling numbers of the first kind and $λ$-Stirling numbers of the first kind. Specifically, we give the recurrence relations for these numbers and show their connections with the $λ$-Stirling numbers of the first kind and higher-order Daehee polynomials.
We introduce the degenerate Bernoulli numbers of the second kind as a degenerate version of the Bernoulli numbers of the second kind. We derive a family of nonlinear differential equations satisfied by a function closely related to the generating function for those numbers. We obtain explicit expressions for the coefficients appearing in those differential equations and the degenerate Bernoulli numbers of the second kind. In addition, as an application and from those differential equations we have an identity expressing the degenerate Bernoulli numbers of the second kind in terms of those numbers of higher-orders.
In this paper, we derive some identities involving special numbers and moments of random variables by using the generating functions of the moments of certain random variables. Here the related special numbers are Stirling numbers of the first and second kinds, degenerate Stirling numbers of the first and second kinds, derangement numbers, higher-order Bernoulli numbers and Bernoulli numbers of the second kind.
Recently, the degenerate Stirling numbers of the first kind were introduced. In this paper, we give some formulas for the degenerate Stirling numbers of the first kind in the terms of the complete Bell polynomials with higher-order harmonic number arguments. Also, we derive an identity connecting the degenerate Stirling numbers of the first kind and the degenerate derangement numbers by using probabilistic method.
In combinatorics, a derangement is a permutation that has no fixed points. The number of derangements of an n-element set is called the n-th derangement number. In this paper, as natural companions to derangement numbers and degenerate versions of the companions we introduce derangement polynomials and degenerate derangement polynomials. We give some of their properties, recurrence relations and identities for those polynomials which are related to some special numbers and polynomials.
In this paper, we consider the degenerate Changhee numbers and polynomials of the second kind which are different from the previously introduced degenerate Changhee numbers and polynomials by Kwon-Kim-Seo (see [11]). We investigate some interesting identities and properties for these numbers and polynomials. In addition, we give some new relations between the degenerate Changhee polynomials of the second kind and the Carlitz's degenerate Euler polynomials.
In this paper, we consider the degenerate Daehee numbers and polynomials of the second kind which are different from the previously introduced Daehee numbers and polynomials. We investigate some properties of these numbers and polynomials. In addition, we give some new identities and relations between the Daehee polynomials of the second kind and Carlitz's degenerate Bernoulli polynomials.
In a recent work, the degenerate Stirling polynomials of the second kind were studied by T. Kim. In this paper, we investigate the extended degenerate Stirling numbers of the second kind and the extended degenerate Bell polynomials associated with them. As results, we give some expressions, identities and properties about the extended degener- ate Stirling numbers of the second kind and the extended degenerate Bell polynomials.
Recently, several authors have studied the Stirling numbers of the second kind and Bell polynomials. In this paper, we study the extended Stirling polynomials of the second kind and the extended Bell polynomials associated with the Stirling numbers of the second kind. In addition, we note that the extended Bell polynomials can be expressed in terms of the moments of the Poisson random variable with parameter
In this paper, we study the degenerate Eulerian polynomials and numbers and give some new and interesting identities associated with several special numbers and polynomials.
In this paper, we study degenerate ordered Bell polynomials with the viewpoint of Carlitz's degenerate Bernoulli and Euler polynomials and derive by using umbral calculus some properties and new identities for the degenerate ordered Bell polynomials associated with special polynomials.
The purpose of this paper is to give some symmetric identities of higher-order degenerate Euler polynomials derived from the symmetric properties of the multivariate p-adic fermionic integrals on Zp.
In this paper, we consider the degenerate Stirling polynomials of the second kind which are derived from the generating function. In addition, we give some new identities for these polynomials.
In this paper, we introduce the degenerate Laplace transform and degenerate gamma function and investigate some properties of the degenerate Laplace transform and degenerate gamma function. From our investigation, we derive some interesting formulas related to the degenerate Laplace transform and degenerate gamma function.