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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 Theory · Mathematics 2018-02-06 Taekyun Kim , Dae San Kim

In recent years, some degenerate versions of quite a few special numbers and polynomials are introduced and investigated by means of various methods. The aim of this paper is to study some results on degenerate harmonic numbers, degenerate…

Number Theory · Mathematics 2022-08-30 Taekyun Kim , Dae San Kim

Many works have been done in recent years as to explorations for degenerate versions of some special polynomials and numbers, which began with the introduction of the degenerate Bernoulli and degenerate Euler polynomials by Carlitz. The aim…

Number Theory · Mathematics 2022-12-13 Taekyun Kim , Dae San Kim , Jongkyum Kwon

The first aim of this paper is to construct new generating functions for the generalized {\lambda}-Stirling type numbers of the second kind, generalized array type polynomials and generalized Eulerian type polynomials and numbers, attached…

Number Theory · Mathematics 2018-11-19 Yilmaz Simsek

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…

Number Theory · Mathematics 2019-08-30 Taekyun Kim , Dae san Kim , Lee-Chae Jang , Han-Young Kim

Sequences of Genocchi numbers of the first and second kind are considered. For these numbers, an approach based on their representation using sequences of polynomials is developed. Based on this approach, for these numbers some identities…

Combinatorics · Mathematics 2019-11-26 Andrei K. Svinin

Recently, several authors have studied the degenerate Bernoulli and Euler polynomials and given some intersting identities of those polynomials. In this paper, we consider the degenerate Bell numbers and polynomials and derive some new…

Number Theory · Mathematics 2015-07-09 Taekyun Kim , Dae san Kim

The purpose of this paper is to give some new identities for the Bernoulli, the Euler and the Genocchi numbers and polynomials.

Number Theory · Mathematics 2009-12-31 Taekyun Kim

The multi-Stirling numbers of the second kind, the unsigned multi-Stirling numbers of the first kind, the multi-Lah numbers and the multi-Bernoulli numbers are all defined with the help of the multiple logarithm, and generalize respectively…

Number Theory · Mathematics 2023-03-02 Taekyun Kim , Dae San Kim , Hye Kyung Kim

In this paper, a new form of poly-Genocchi polynomials is defined by means of poly-logarithm, namely, the Apostol-type poly-Genocchi polynomials of higher order with parameters a, b and c. Several properties of these polynomials are…

Combinatorics · Mathematics 2020-09-09 Cristina B. Corcino , Roberto B. Corcino

In this paper we present the generalization of the higher order q-Euler numbers and q-Genocchi numbers and w-Genocchi numbers and polynomials of high order using the multivariate fermionic p-adic integral on Zp. We have the interpolation…

Number Theory · Mathematics 2009-01-14 Taekyun Kim , Young-hee Kim , Kyoung-won Hwang

By considering Eulerian numbers and ordered Stirling numbers of the second and third kinds over a multiset, we generalize identities of Eulerian numbers and Stirling numbers of the second and third kinds and provide $q$-analogs of these…

Combinatorics · Mathematics 2012-09-07 Joon Yop Lee

This paper has two primary contributions. First, we explore degenerate Sheffer-type polynomials, a hybrid of higher-order degenerate Bernoulli and Euler polynomials, and derive their properties. Second, assuming that the moment generating…

Number Theory · Mathematics 2025-07-29 Taekyun Kim , Dae san Kim

In this paper, we establish more identities of generalized multi poly-Euler polynomials with three parameters and obtain a kind of symmetrized generalization of the polynomials. Moreover, generalized multi poly-Bernoulli polynomials are…

Number Theory · Mathematics 2018-07-25 Roberto B. Corcino , Hassan Jolany , Cristina B. Corcino , Takao Komatsu

We study matrices which transform the sequence of Fibonacci or Lucas polynomials with even index to those with odd index and vice versa. They turn out to be intimately related to generalized Stirling numbers and to Bernoulli, Genocchi and…

Combinatorics · Mathematics 2011-03-15 Johann Cigler

In this paper, we will define general Eulerian numbers and Eulerian polynomials based on general arithmetic progressions. Under the new definitions, we have been successful in extending several well-known properties of traditional Eulerian…

Combinatorics · Mathematics 2012-07-03 Tingyao Xiong , Hung-ping Tsao , Jonathan I. Hall

The aim of this paper is to study the degenerate Bell numbers and polynomials which are degenerate version of the Bell numbers and polynomials. we derive some new identities and properties of those numbers and polynomials that are…

Number Theory · Mathematics 2021-08-16 Taekyun Kim , Dae San Kim , Hyunseok Lee , Seongho Park

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…

Number Theory · Mathematics 2017-08-01 Taekyun Kim , Dae San Kim

In the paper, the authors review some explicit formulas and establish a new explicit formula for Bernoulli and Genocchi numbers in terms of Stirling numbers of the second kind.

Number Theory · Mathematics 2015-02-24 Bai-Ni Guo , Feng Qi

This paper introduces and investigates degenerate versions of the A-algorithm and B-algorithm by incorporating a parameter lambda into their respective recurrence relations. We derive explicit formulas for the final sequences of these…

Number Theory · Mathematics 2026-01-05 Taekyun Kim , Dae san Kim