A New Proof of Stirling's Formula

TL;DR

This paper presents a novel, straightforward proof of Stirling's formula using the partial fraction expansion of the tangent function, offering a fresh perspective on a classical asymptotic approximation.

Contribution

It introduces a new simple proof of Stirling's formula based on tangent function partial fractions, differing from traditional methods.

Findings

Provides a concise proof of Stirling's formula

Utilizes partial fraction expansion of tangent function

Offers an alternative approach to classical asymptotic analysis

Abstract

A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.