arXiv subjects

Addisalem Abathun

Publications and source records attributed to Addisalem Abathun.

2 recordsLinked to original sources

arXiv2014

Zeros of a certain class of Gauss hypergeometric polynomials

In this paper, we give results that partially prove a conjecture which was discussed in our previous work (arXiv:1307.4991). More precisely, we prove that as $n\to \infty,$ the zeros of the polynomial$${}_{2}\text{F}_{1}\left[ \begin{array}{c} -n, αn+1\\ αn+2 \end{array} ; \begin{array}{cc} z \end{array}\right]$$ cluster on a certain curve defined as a part of a level curve of an explicit harmonic function. This generalizes work by Boggs, Driver, Duren et. al, to a complex parameter $α$.

math.CV↗

arXiv2013

Asymptotic distribution of zeros of a certain class of hypergeometric polynomials

We study the weak asymptotic behavior of the zeros of a family of a certain class of (generalized) hypergeometric polynomials, using the associated hypergeometric differential equation, as the parameters go to infinity. We describe the curve complex on which the zeros cluster, as level curves associated to integrals on an algebraic curve derived from the equation. In a certain degenerate case we make a precise conjecture, based and generalizing work by Duren, Driver et. al, and present experimental evidence for it.

math.CV↗