Zobrazeno 1 - 10
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pro vyhledávání: '"Kim, Taekyun"'
Autor:
Kim, Taekyun, Kim, Dae San
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 called the nth derangement number. Recently, the degenerate derangement
Externí odkaz:
http://arxiv.org/abs/2410.09394
Autor:
Kim, Taekyun, Kim, Dae San
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 identities involve Euler numbers and are obtained by computing the momen
Externí odkaz:
http://arxiv.org/abs/2410.05895
Law evolves with society. As population growth and social changes give rise to new issues and conflicts, additional laws are introduced into the existing legal system. These new laws not only expand the volume of the system but can also disrupt it by
Externí odkaz:
http://arxiv.org/abs/2410.04493
In recent years, both degenerate versions and probabilistic extensions of many special numbers and polynomials have been explored. For instance, degenerate Bernstein polynomials and probabilistic Bernstein polynomials were investigated earlier. Assum
Externí odkaz:
http://arxiv.org/abs/2410.04464
Autor:
Kim, Taekyun, kim, Dae San
In this paper, we study several degenerate trigonometric functions, which are degenerate versions of the ordinary trigonometric functions, and derive some identities among such functions by using elementary methods. Especially, we obtain multiple ang
Externí odkaz:
http://arxiv.org/abs/2410.01199
Autor:
Kim, Taekyun, Kim, Dae san
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 version of the recent probabilistic proofs on sums of powers of integers.<
Externí odkaz:
http://arxiv.org/abs/2409.07742
Autor:
Kim, Taekyun, Kim, Dae San
In this paper, we derive by using elementary methods some continued fractions, certain identities involving derivatives of tanx, several expressions for log coshx and an identity for {\pi}2, from a series expansion of tan x, which gives the product e
Externí odkaz:
http://arxiv.org/abs/2407.19885
Autor:
Kim, Taekyun, Kim, Dae San
Let X be the Laplacian random variable with parameters (a,b)=(0,1), and let X1, X2, X3 , ...be a sequence of mutually independent copies of X$. In this note, we explicitly determine the moments of the Laplacian random variable in terms of the Bernoul
Externí odkaz:
http://arxiv.org/abs/2407.13150
Autor:
Kim, Taekyun, Kim, Dae san
Assume that the moment generating function of the random vari able Y exists in a neighborhood of the origin. We introduce the probabilistic multi-Stirling numbers of the second kind associated with Y and the proba bilistic multi-Lah numbers associate
Externí odkaz:
http://arxiv.org/abs/2407.00061
Autor:
Kim, Taekyun, Kim, Dae san
Let Y be a random variable whose degenerate moment generating functions exist in some neighborhoods of the origin. The aim of this paper is to study the probabilistic degenerate Stirling numbers of the first kind associated with Y which are construct
Externí odkaz:
http://arxiv.org/abs/2406.06945