Gwan-Woo Jang

Degenerate r-Stirling Numbers and r-Bell Polynomials

The purpose of this paper is to exploit umbral calculus in order to derive some properties, recurrence relations, and identities related to the degenerate r-Stirling numbers of the second kind and the degenerate r-Bell polynomials. Especially, we will express the degenerate r-Bell polynomials as linear combinations of many well-known families of special polynomials.

Symmetric Identities for Fubini Polynomials

We represent the generating function of w-torsion Fubini polynomials by means of a fermionic p-adic integral on Zp. Then we investigate a quotient of such p-adic integrals on Zp, representing generating functions of three w-torsion Fubini polynomials and derive some new symmetric identities for the w-torsion Fubini and two variable w-torsion Fubini polynomials.

Fourier series of finite products of Bernoulli and Genocchi functions

In this paper, we consider three types of functions given by products of Bernoulli and Genocchi functions and derive some new identities arising from Fourier series expansions associated with Bernoulli and Genocchi functions. Furthermore, we will express each of them in terms of Bernoulli functions.

The Partially Degenerate Changhee-Genocchi Polynomials and Numbers

In this paper, we introduce the partially degenerate ChangheeGenocchi polynomials and numbers and investigated some identities of these polynomials. Furthermore, we investigate some explicit identities and properties of the partially degenerate Changhee-Genocchi arising from the nonlinear differential equations.

A note on some identities of derangement polynomials

The problem of counting derangements was initiated by Pierre Rémond de Montmort in 1708 (see Carlitz in Fibonacci Q. 16(3):255–258, 1978, Clarke and Sved in Math. Mag. 66(5):299–303, 1993, Kim, Kim and Kwon in Adv. Stud. Contemp. Math. (Kyungshang) 28(1):1–11 2018. A derangement is a permutation that has no fixed points, and the derangement number dn

Fourier series of higher-order ordered Bell functions

d_{n}

Fourier series of functions involving higher-order ordered Bell polynomials

is the number of fixed-point-free permutations on an n element set. In this paper, we study the derangement polynomials and investigate some interesting properties which are related to derangement numbers. Also, we study two generalizations of derangement polynomials, namely higher-order and r-derangement polynomials, and show some relations between them. In addition, we express several special polynomials in terms of the higher-order derangement polynomials by using umbral calculus.

Series of sums of products of higher-order Bernoulli functions

In this paper, we consider higher-order ordered Bell functions and derive their Fourier series expansions. Moreover, we express those functions in terms of Bernoulli functions. c ©2017 All rights reserved.

Sums of finite products of Genocchi functions

Abstract In 1859, Cayley introduced the ordered Bell numbers which have been used in many problems in number theory and enumerative combinatorics. The ordered Bell polynomials were defined as a natural companion to the ordered Bell numbers (also known as the preferred arrangement numbers). In this paper, we study Fourier series of functions related to higher-order ordered Bell polynomials and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.

Some identities of degenerate Daehee numbers arising from nonlinear differential equation

It is shown in a previous work that Faber-Pandharipande-Zagier’s and Miki’s identities can be derived from a polynomial identity, which in turn follows from the Fourier series expansion of sums of products of Bernoulli functions. Motivated by and generalizing this, we consider three types of functions given by sums of products of higher-order Bernoulli functions and derive their Fourier series expansions. Moreover, we express each of them in terms of Bernoulli functions.