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Seon-Hong Kim

Publications and source records attributed to Seon-Hong Kim.

4 recordsLinked to original sources
arXiv2026

Properties of two Chebyshev-like polynomial sequences

By modifying the generating function of the Chebyshev polynomials of the second kind, we obtain a sequence of reciprocal (or palindromic) polynomials, as well as a related companion sequence. Among numerous other properties, we obtain discriminant and resultant identities for these polynomial sequences and prove partial irreducibility results. Throughout, we point to parallels and connections with the Chebyshev polynomials of both kinds.

math.CA↗
arXiv2025

A Balanced Three-term Generalization of Nicomachus' Identity

We present a generalization of the classical Nicomachus' identity for the sum of the first $n$ cubes. Unlike previous generalizations, it has three rather than two terms, and involves not just one, but two distinct triangular numbers, and each term is of degree $4$ in $\lfloor n/2 \rfloor$. The asymptotic behavior for large $n$ leads to continued fractions with remarkable (but conjectural) properties. Moreover, we give a way of looking at squares of triangular numbers that involves the square root of $11$ and show it is a limiting case of a non-obvious identity involving truncations of the continued fraction expansion of that square root. The details involve a nonlinear recurrence that (with appropriate initial conditions) unexpectedly produces only integers, a ``Somos-type'' phenomenon.

math.NT↗
arXiv2023

Translations and extensions of the Nicomachus identity

We search for Nicomachean identities by adding translation parameters, variable parameters, sequence products and adjoining further numbers to sequences. The solutions of definite and indefinite quadratic forms arise in this study of cubic equations obtained from translation parameters. Our search leads to many general Nicomachean-type identities. We also study the geometry of adjoining two numbers to sequences satisfying the Nicomachean identity.

math.NT↗