106 citations · 573 across the 226 of their papers we have counts for
16 papers · 1 filter
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…
Probabilistic proof of a summation formula
Taekyun Kim, Dae San Kim
The aim of this paper is to derive a summation formula for the alternating infinite series and an expression for zeta function by using hyperbolic secant random variables. These id…
Probabilistic degenerate Bernstein polynomials
Jinyu Wang, Yuankui Ma, Taekyun Kim +1
In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials an…
Some identities on degenerate trigonometric functions
Taekyun Kim, Dae San kim
In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such fun…
A probabilistic proof of a recurrence relation for sums of values of degenerate falling factorials
Taekyun Kim, Dae san Kim
In this paper, we consider sums of values of degenerate falling factorials and give a probabilistic proof of a recurrence relation for them. This may be viewed as a degenerate vers…