48 citations · 54 across the 40 of their papers we have counts for
35 papers · 1 filter
Generalized Bell polynomial operators arising from generalized normal ordering
Taekyun Kim, Dae san Kim
This paper explores the deformed combinatorial structures arising from the generalized Heisenberg algebra GHA which is characterized by an analytic function of the Hamiltonian f(H)…
Degenerate generalized Stirling operators of the first kind arising from generalized Heisenberg algebra
Taekyun Kim, Dae San Kim
This paper investigates the degenerate generalized Stirling operators of the first kind bridging a gap in the operational calculus of the generalized Heisenberg algebra GHA unified…
A note on Leibniz rule for difference quotient
Taekyun Kim, Dae san Kim
In this note, we derive a Leibniz rule for difference quotient.
Logarithms and Stirling numbers associated with delta series
Dae san Kim, Taekyun Kim
This paper investigates the Stirling numbers of the first and second kind associated with a delta series f (t). These numbers provide a robust framework that satisfies the orthogon…
Probabilistic degenerate logarithm and heterogeneous stirling numbers
Dae San Kim, Taekyun Kim
Let Y be a random variable whose moment-generating function exists in some neighborhood of the origin. While probabilistic Stirling numbers of the first and second kind have been i…
Probabilistic heterogeneous Stirling numbers and Bell polynomials
Taekyun Kim, Dae San Kim
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabi…
Degenerate Algorithms for degenerate Bernoulli and Euler numbers
Taekyun Kim, Dae san Kim
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 der…
Degenerate Euler- Seidel Method for degenerate Bernoulli, Euler, and Genocchi polynomials
Taekyun Kim, Dae San Kim, Hyunseok Lee +1
This paper introduces a degenerate version of the Euler-Seidel method by incorporating a parameter lambda into the classical recurrence relation. We define a degenerate Euler-Seide…
Degenerate Euler-Seidel Matrix Method and Their Applications
Taekyun Kim, Dae san Kim
This paper introduces a degenerate version of the Euler-Seidel matrix method by incorporating a parameter lambda into the classical recurrence relation. The standard Euler-Seidel m…
Probabilistic Stirling numbers associated with sequences
Dae San Kim, Taekyun Kim
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. Recently, probabilistic Stirling numbers of the first kind and of the second kin…
Representations by probabilistic Bernoulli and degenerate Bernoulli polynomials
Dae san Kim, Taekyun Kim
We investigate the representation of arbitrary polynomials using probabilistic Bernoulli and degenerate Bernoulli polynomials associated with a random variable , whose moment ge…
Recurrence relations for harmonic and derangement numbers
Taekyun Kim, Dae san Kim, Jongkyum Kwon +1
We use elementary methods to establish three key recurrence relations: one for derangement numbers, a second for harmonic numbers, and a third for degenerate harmonic numbers. Our…
Spivey-type recurrence relation for fully degenerate Bell polynomials
Taekyun Kim, Dae San Kim
Spivey's combinatorial method revealed an important identity for Bell numbers, involving Stirling numbers of the second kind. This paper extends his work by deriving Spivey-type re…
A note on new type degenerate Srirling numbers of the first kind
Taekyun Kim, Dae san Kim, Kyo-Shin Hwang +1
We introduce a new sequence of unsigned degenerate Stirling numbers of the first kind. Following the work of Adell-Lekuona, who represented unsigned Stirling numbers of the first k…
Probabilistic generalization of Spivey-type relation for degenerate Bell polynomials
Taekyun Kim, Dae San Kim
Following Spivey's pivotal discovery of a recurrence relation for Bell numbers, significant research has emerged concerning various generalizations of Bell numbers and polynomials.…
Representations by probabilistic Frobenius-Euler and degenerate Frobenius-Euler polynomials
Taekyun Kim, Dae San Kim
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to represent arbitrary polynomials in terms of probabil…
Several expressions for degenerate harmonic numbers and some related numbers
Taekyun Kim, Dae san Kim, Kyo-Shin Hwang
Many authors have recently studied the degenerate harmonic numbers. This paper makes two main contributions. First, we derive several explicit expressions for these numbers, which…
Degenerate Sheffer-type polynomials and degenerate Sheffer polynomials associated with a random variable
Taekyun Kim, Dae san Kim
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 the…
Probabilistic degenerate poly-Bell polynomials associated with random variables
Pengxiang Xue, Yuankui Ma, Taekyun Kim +2
Let Y be a random variable whose moment generating function exists in a neighborhood of the origin. The aim of this paper is to study the probabilistic degenerate poly-Bell polynom…
Recurrence relations for degenerate Bell and Dowling polynomials via Boson operators
Taekyun Kim, Dae San Kim
Spivey found a recurrence relation for the Bell numbers by using combinatorial method. The aim of this paper is to derive Spivey's type recurrence relations for the degenerate Bell…
Spivey's type recurrence relation for degenerate Bell polynomials
Taekyun Kim, Dae San Kim
The aim of this paper is to derive a recurrence relation for the degenerate Bell polynomials by using the operators X and D satisfying the commutation relation DX-XD=1. Here X is t…
Combinatorial identities related to degenerate Stirling numbers of the second kind
Taekyun Kim, Dae san Kim
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 rec…
Degenerate Eulerian polynomials and numbers
Taekyun Kim, Dae san Kim
The aim of this paper is to study degenerate Eulerian polynomials and degenerate Eulerian numbers, respectively as degenerate versions of the Eulerian polynomials and the Eulerian…
Probabilistic degenerate derangement polynomials
Taekyun Kim, Dae San Kim
In combinatorics, a derangement is a permutation of the elements of a set, such that no element appears in its original position. The number of derangement of an n-element set is c…