26 papers
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…