3 citations · 6 across the 9 of their papers we have counts for
12 papers
On the zeros of certain Sheffer sequences and their cognate sequences
Gi-Sang Cheon, Tamás Forgács, Khang Tran
Given a Sheffer sequence of polynomials, we introduce the notion of an associated sequence called the cognate sequence. We study the relationship between the zeros of this pair of…
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 , where $α, β, c \in…
An exploration of very triangular numbers
Audrey Baumheckel, Tamás Forgács
We present a collection of results concerning the location and distribution of very triangular numbers among triangular numbers, including the twin very triangular number theorem,…
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 , where is a quadratic polynomi…
Hyperbolic polynomials and linear-type generating functions
Tamás Forgács, Khang Tran
We prove that the polynomials generated by the relation are hyperbolic for given that the zeros o…
A note on series with recursively defined terms
Tamás Forgács, Jack Luong, Joshua Williamson
In this note we study the convergence of recursively defined infinite series. We explore the role of the derivative of the defining function at the origin (if it exists), and devel…
On Zero-Sector Reducing Operators
David A. Cardon, Tamás Forgács, Andrzej Piotrowski +2
We prove a Jensen-disc type theorem for polynomials having all their zeros in a sector of the complex plane. This result is then used to prove the existence of…
Sufficient conditions for a linear operator on to be monotone
Leah Buck, Kelly Emmrich, Tamás Forgács
We demonstrate that being a hyperbolicity preserver does not imply monotonicity for infinite order differential operators on , thereby settling a recent conjecture i…
On the zeros of polynomials generated by rational functions with a hyperbolic polynomial type denominator
Tamás Forgács, Khang Tran
This paper investigates the location of the zeros of a sequence of polynomials generated by a rational function with a denominator of the form , where the zeros…
Multiplier sequences, classes of generalized Bessel functions and open problems
George Csordas, Tamás Forgács
Motivated by the study of the distribution of zeros of generalized Bessel-type functions, the principal goal of this paper is to identify new research directions in the theory of m…
The non-existence of cubic Legendre multiplier sequences
Tamás Forgács, James Haley, Rebecca Menke +1
The main result in this paper is the proof of the recently conjectured non-existence of cubic Legendre multiplier sequences. We also give an alternative proof of the non-existence…
Multiplier Sequences for Generalized Laguerre Bases
Tamás Forgács, Andrzej Piotrowski
In this paper we present a complete characterization of geometric and linear multiplier sequences for generalized Laguerre bases. In addition, we give a partial characterization of…