An Elementary Proof of Stirling's Formula
Jakub Smol\'ik
TL;DR
This paper offers a new, elementary proof of Stirling's formula for factorial approximation, relying solely on limits and the Wallis product, avoiding integral calculus.
Contribution
It introduces a novel proof method for Stirling's formula using basic limit techniques and the Wallis product, simplifying the understanding of the approximation.
Findings
Proof avoids integral calculus
Uses only limits and Wallis product
Simplifies understanding of Stirling's formula
Abstract
Stirling's formula is a powerful asymptotic approximation of the factorial function. Many well-known proofs of this formula are grounded in integral calculus. In this paper, we present an alternative proof of Stirling's formula using only limits and the Wallis product.
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Taxonomy
TopicsFunctional Equations Stability Results · Mathematics and Applications · Scientific Measurement and Uncertainty Evaluation