Properties of certain sequences related to Stirling's approximation for the gamma function
type: Item
instance of: scholarly article
title: Properties of certain sequences related to Stirling's approximation for the gamma function
zbMATH Open document ID: 1044.33001
DOI: 10.1016/S0723-0869(03)80017-8
author: Paul Bracken
published in: Expositiones Mathematicae
publication date: 2004-03-17T00:00:00Z
review text: The monotonicity properties of certain sequences related to the Stirling formula are studied. Put \(n!= T_n\cdot S_n\), where \(S_n= \sqrt{2\pi n}\cdot({n\over e})^n\). Let \(a_n= 12n- 1/(T_n-1)\) and \(b_n= n({1\over 2}- a_n)\). Then the sequences \((a_n)\) and \((b_n)\) are strictly increasing. The first terms in the asymptotic expansion of \(a_n\) are also given. For example, \(\lim_{n\to\infty} a_n={1\over 2}\), \(\lim_{n\to\infty} b_n= {293\over 720}\).
reviewed by: József Sándor
Mathematics Subject Classification ID: 33B15
zbMATH DE Number: 2059471
zbMATH Keywords: Stirling's formula
zbMATH Keywords: Gamma function
MaRDI profile type: Publication
cites work: Analytic Inequalities
cites work: Q5603342
description: scientific article; zbMATH DE number 2059471