An alternative proof of Elezovi\'c-Giordano-Pe\v{c}ari\'c's theorem

TL;DR

This paper provides a new proof for a theorem related to bounds in Gautschi's inequality, offering an alternative approach to a known mathematical result.

Contribution

It introduces an alternative proof for Elezović-Giordano-Pečarić's theorem, expanding the methods available for understanding bounds in Gautschi's inequality.

Findings

New proof simplifies understanding of the theorem

Provides an alternative approach to existing proofs

Enhances mathematical tools for inequalities

Abstract

In the present note, an alternative proof is supplied for Theorem~1 in [N. Elezovi\'c, C. Giordano and J. Pe\v{c}ari\'c, \textit{The best bounds in Gautschi's inequality}, Math. Inequal. Appl. \textbf{3} (2000), 239\nobreakdash--252.].