From the 1 of 31 linked papers with an AI index.
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On Generalized Chebyshev polynomials
Taekyun Kim, Dae San Kim
In this paper, we introduce and study a novel family of generalized Chebyshev polynomials defined via a rational generating function. We demonstrate that the classical Chebyshev po…
Study on Morgan-Voyce type polynomials with Euler-Seidel algorithm
Taekyun Kim, Dae san Kim
The paper defines new families of Morgan‑Voyce type polynomials, derives their explicit formulas, recurrence relations and exponential generating functions, and links them to Euler…
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…