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

**ON THE HYPERFACTORIAL FUNCTION,**

HYPERTRIANGULAR FUNCTION, AND

THE DISCRIMINANTS OF CERTAIN POLYNOMIALS

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.

**Received: **February 9, 2007

**AMS Subject Classification: **11A

**Key Words and Phrases: **-th roots of unity, hyperfactorial function, hypertriangular function, function, the discriminant of a polynomial, Barnes function, Euler gamma function, Sylvester matrix, resultant of two polynomials

**Source:** International Journal of Pure and Applied Mathematics

**ISSN:** 1311-8080

**Year:** 2007

**Volume:** 36

**Issue:** 2