The Newton integral and the Stirling formula
History and Overview
2019-07-08 v1 Classical Analysis and ODEs
Combinatorics
Abstract
We present details of logically simplest integral sufficient for deducing the Stirling asymptotic formula for n!. It is the Newton integral, defined as the difference of values of any primitive at the endpoints of the integration interval. We review in its framework in detail two derivations of the Stirling formula. The first approximates log(1)+log(2)+...+log(n) with an integral and the second uses the classical gamma function and a Fubini-type result. We mention two more integral representations of n!.
Cite
@article{arxiv.1907.02553,
title = {The Newton integral and the Stirling formula},
author = {Martin Klazar},
journal= {arXiv preprint arXiv:1907.02553},
year = {2019}
}
Comments
25 pages