Results 1 to 10 of about 106 (95)

Study on r-Truncated Degenerate Stirling Numbers of the Second Kind

Open Mathematics, 2022
The degenerate Stirling numbers of the second kind and of the first kind, which are, respectively, degenerate versions of the Stirling numbers of the second kind and of the first kind, appear frequently when we study various degenerate versions of some ...
Taekyun Kim, Dae San Kim
exaly   +4 more sources

Some Identities Related to Degenerate Stirling Numbers of the Second Kind

Demonstratio Mathematica, 2022
The degenerate Stirling numbers of the second kind were introduced as a degenerate version of the ordinary Stirling numbers of the second kind. They appear very frequently when one studies various degenerate versions of some special numbers and ...
Taekyun Kim, Hye Kyung Kim, Dae San Kim
exaly   +3 more sources

Identities Involving Degenerate Stirling Numbers of the Second Kind

Mathematical and Computer Modelling of Dynamical Systems
Building on Carlitz’s foundational work with degenerate Euler and Bernoulli polynomials, recent research has introduced and studied various degenerate special numbers and polynomials.
Taekyun Kim
exaly   +4 more sources

A Note on Degenerate r-Stirling Numbers

Journal of Inequalities and Applications, 2020
The aim of this paper is to study the unsigned degenerate r-Stirling numbers of the first kind as degenerate versions of the r-Stirling numbers of the first kind and the degenerate r-Stirling numbers of the second kind as those of the r-Stirling numbers ...
Taekyun Kim, Dae San Kim, Jin-Woo Park
exaly   +3 more sources

Generalized Degenerate Stirling Numbers Arising From Degenerate Boson Normal Ordering

Applied Mathematics in Science and Engineering, 2023
It is remarkable that, in recent years, intensive studies have been done for degenerate versions of many special polynomials and numbers and have yielded many interesting results.
Taekyun Kim, Hye Kyung Kim, Dae San Kim
exaly   +2 more sources

Combinatorial Identities Related to Degenerate Stirling Numbers of the Second Kind

Proceedings of the Steklov Institute of Mathematics
The study of degenerate versions of certain special polynomials and numbers, which was initiated by Carlitz's work on degenerate Euler and degenerate Bernoulli polynomials, has recently seen renewed interest among mathematicians. The aim of this paper is to study some properties, certain identities, recurrence relations and explicit expressions for ...
Taekyun Kim, Dae San Kim
exaly   +3 more sources

Evaluation of Cauchy Polynomials via Degenerate r -Stirling Numbers

Mathematical and Computer Modelling of Dynamical Systems
In this paper, within the framework of unsigned degenerate [Formula: see text]-Stirling numbers, we establish connections among Cauchy polynomials, degenerate Bernoulli polynomials, and degenerate hyperharmonic numbers.
Taekyun Kim, Yuankui Ma, Yanan Hei
exaly   +3 more sources

Probabilistic Poly Degenerate r-Stirling Numbers of the Second Kind and r-Bell Polynomials

European Journal of Pure and Applied Mathematics
We introduce degenerate poly r-Stirling numbers of the second kind and poly r-Bell polynomials by using degenerate polyexponential function and investigate some properties of these number and polynomials.
exaly   +2 more sources

Fully degenerate Bernoulli numbers and polynomials

Demonstratio Mathematica, 2022
The aim of this article is to study the fully degenerate Bernoulli polynomials and numbers, which are a degenerate version of Bernoulli polynomials and numbers and arise naturally from the Volkenborn integral of the degenerate exponential functions on Zp{
Kim Taekyun, Kim Dae San, Park Jin-Woo
doaj   +1 more source

Generalized degenerate Bernoulli numbers and polynomials arising from Gauss hypergeometric function

Advances in Difference Equations, 2021
A new family of p-Bernoulli numbers and polynomials was introduced by Rahmani (J. Number Theory 157:350–366, 2015) with the help of the Gauss hypergeometric function.
Taekyun Kim, Dae San Kim, Lee-Chae Jang, Hyunseok Lee, Hanyoung Kim   +4 more
doaj   +1 more source