A refinement of Ramanujan's factorial approximation

被引：17

作者：

Hirschhorn, Michael D. ^{[1
]}

Villarino, Mark B. ^{[2
]}

机构：

[1] Univ New S Wales, Sch Math & Stat, Sydney, NSW 2052, Australia

[2] Univ Costa Rica, Escuela Matemat, San Jose 11501, Costa Rica

来源：

RAMANUJAN JOURNAL | 2014年 / 34卷 / 01期

关键词：

Ramanujan; Stirling's formula; GAMMA FUNCTION;

D O I：

10.1007/s11139-013-9494-y

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We present a new proof of the monotonicity of the correction term theta(n) in Ramanujan's refinement of Stirling's formula. Moreover we prove that theta(n) is concave.

引用

页码：73 / 81

页数：9

共 5 条

[1] On Ramanujan's double inequality for the gamma function [J].

Alzer, H .

BULLETIN OF THE LONDON MATHEMATICAL SOCIETY, 2003, 35 :601-607

[2] A new version of Stirling's formula [J].

Hirschhorn, Michael .

MATHEMATICAL GAZETTE, 2006, 90 (518) :286-292

[3] On the asymptotic representation of the Euler gamma function by Ramanujan [J].

Karatsuba, EA .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2001, 135 (02) :225-240

[4]

Ramanujan S., 1987, The Lost Notebook and Other Unpublished Papers

[5]

Villarino M.B., 2013, MATH GAZ IN PRESS, V97

← 1 →