# IJPAM: Volume 36, No. 2 (2007)

ON THE HYPERFACTORIAL FUNCTION,
HYPERTRIANGULAR FUNCTION, AND
THE DISCRIMINANTS OF CERTAIN POLYNOMIALS

Department of Mathematics
University of Evansville
1800 Lincoln Avenue, Evansville, IN 47722, USA
e-mail: azarian@evansville.edu

Abstract.For any natural number , let be the hyperfactorial function of , and let , be the hypertriangular function of Also, let represent the roots of the polynomial equation (for a fixed ). First, we show that (for any integer ) can be written in terms of the discriminant of Then, we use this result to show that and can be written as a product of discriminants of certain polynomials, and as a sum of discriminants of these polynomials, respectively. Also, we use a known result to present an upper and a lower bound for Finally, we pose two questions for the reader.