Khang Tran

activity

20162022

collaborators

7 papers

math.CO2022

The zero locus and some combinatorial properties of certain exponential Sheffer sequences

Gi-Sang Cheon, Tamás Forgács, Arnauld Mesinga Mwafise +1

We present combinatorial and analytical results concerning a Sheffer sequence with an exponential generating function of the form $G (s, z) = e^{cz s + α z^{2} + β z^{4}}$ , where $α, β, c \in…

math.CO2021

On combinatorial properties and the zero distribution of certain Sheffer sequences

Gi-Sang Cheon, Tamás Forgács, Hana Kim +1

We present combinatorial and analytical results concerning a Sheffer sequence with a generating function of the form $G (x, z) = Q (z)^{x} Q (- z)^{1 - x}$ , where $Q$ is a quadratic polynomi…

math.CA2020

Zeros of a binomial combination of Chebyshev polynomials

Summer Al Hamdani, Khang Tran

For $0 < α < 1$ , we study the zeros of the sequence of polynomials ${P_{m} (z)}_{m = 0}^{\infty}$ generated by the reciprocal of $(1 - t)^{α} (1 - 2 z t + t^{2})$ , expanded as a power…

math.CV2019

Linear combinations of polynomials with three-term recurrence

Khang Tran, Maverick Zhang

We study the zero distribution of the sum of the first $n$ polynomials satisfying a three-term recurrence whose coefficients are linear polynomials. We also extend this sum to a li…

math.CV2018

Hyperbolic polynomials and linear-type generating functions

Tamás Forgács, Khang Tran

We prove that the polynomials generated by the relation $m = 0 \sum \infty H_{m} (z) t^{m} = \frac{1}{P ( t ) + z t ^{r} Q ( t )}$ are hyperbolic for $m ≫ 1$ given that the zeros o…

math.CV2018

Zeros of polynomials with four-term recurrence and linear coefficients

Khang Tran, Andres Zumba

This paper investigates the zero distribution of a sequence of polynomials ${P_{m} (z)}_{m = 0}^{\infty}$ generated by the reciprocal of $1 + c t + B (z) t^{2} + A (z) t^{3}$ wher…