Jongkyum Kwon

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.

Sums of Finite Products of Euler Functions

In this paper, we consider three types of functions given by sums of finite products of Euler functions and derive their Fourier series expansions. In addition, we express each of them in terms of Bernoulli functions.

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.

On the Degenerate

The Changhee numbers and polynomials are introduced by Kim, Kim and Seo (Adv. Stud. Theor. Phys. 7(20):993–1003, 2013), and the generalizations of those polynomials are characterized. In this paper, we investigate a new q-analog of the higher order degenerate Changhee polynomials and numbers. We derive some new interesting identities related to the degenerate (h,q)-Changhee polynomials and numbers.

(h,q)

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.

-Changhee Numbers and 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

The Partially Degenerate Changhee-Genocchi Polynomials and Numbers

d_{n}

A note on some identities of derangement 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.

Fourier series of higher-order ordered Bell 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.

Series of sums of products of higher-order Bernoulli functions

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.