Small Gamma Products with Simple Values

TL;DR

This paper demonstrates that for every odd natural number greater than one, the product of Gamma function values at specific rational points can be expressed as powers of 2 and pi, revealing a new structural property.

Contribution

It introduces a novel partition of rational numbers related to Gamma function products, showing their values simplify to powers of 2 and pi for odd n.

Findings

Gamma product values are powers of 2 and pi for the specified partitions

The partition covers all rational numbers of the form x/2n in lowest terms

The result holds for all odd natural numbers greater than one

Abstract

Our main result shows that for every odd natural number n > 1 there is a partition of the rational numbers, x/2n in lowest terms, in the unit interval, the product of whose Gamma values takes the form of powers of 2 and pi.