Zeros of a certain class of Gauss hypergeometric polynomials

Abathun, Addisalem, and Bøgvad, Rikard. "Zeros of a certain class of Gauss hypergeometric polynomials." Czechoslovak Mathematical Journal 68.4 (2018): 1021-1031. <http://eudml.org/doc/294392>.

@article{Abathun2018,
abstract = {We prove that as $n\rightarrow \infty $, the zeros of the polynomial \[ \_\{2\}\{F\}\_\{1\}\left[ \begin\{matrix\} -n, \alpha n+1\\ \alpha n+2 \end\{matrix\} ; z\right] \] cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter $\alpha $ and partially proves a conjecture made by the authors in an earlier work.},
author = {Abathun, Addisalem, Bøgvad, Rikard},
journal = {Czechoslovak Mathematical Journal},
keywords = {asymptotic zero-distribution; hypergeometric polynomial; saddle point method},
language = {eng},
number = {4},
pages = {1021-1031},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Zeros of a certain class of Gauss hypergeometric polynomials},
url = {http://eudml.org/doc/294392},
volume = {68},
year = {2018},
}

TY - JOUR
AU - Abathun, Addisalem
AU - Bøgvad, Rikard
TI - Zeros of a certain class of Gauss hypergeometric polynomials
JO - Czechoslovak Mathematical Journal
PY - 2018
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 68
IS - 4
SP - 1021
EP - 1031
AB - We prove that as $n\rightarrow \infty $, the zeros of the polynomial \[ _{2}{F}_{1}\left[ \begin{matrix} -n, \alpha n+1\\ \alpha n+2 \end{matrix} ; z\right] \] cluster on (a part of) a level curve of an explicit harmonic function. This generalizes previous results of Boggs, Driver, Duren et al. (1999–2001) to the case of a complex parameter $\alpha $ and partially proves a conjecture made by the authors in an earlier work.
LA - eng
KW - asymptotic zero-distribution; hypergeometric polynomial; saddle point method
UR - http://eudml.org/doc/294392
ER -