Integral representations and complete monotonicity of remainders of the Binet and Stirling formulas for the gamma function

被引：30
作者：
Qi, Feng [1 ,2 ,3 ]
Guo, Bai-Ni [4 ]
机构：
[1] Henan Polytech Univ, Inst Math, Jiaozuo 454010, Henan, Peoples R China
[2] Inner Mongolia Univ Nationalities, Coll Math, Tongliao 028043, Inner Mongolia, Peoples R China
[3] Tianjin Polytech Univ, Coll Sci, Dept Math, Tianjin 300387, Peoples R China
[4] Henan Polytech Univ, Sch Math & Informat, Jiaozuo 454010, Henan, Peoples R China
来源：
REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS | 2017年 / 111卷 / 02期
关键词：
Remainder; Binet formula; Stirling formula; Gamma function; Complete monotonicity; Integral representation; Limit; LOGARITHM; PROPERTY; RATIO;
D O I：
10.1007/s13398-016-0302-6
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In the paper, the authors find integral representations, complete monotonicity, limits, and other properties of remainders of the Binet and Stirling formulas for the gamma function and their derivatives. These properties strengthen almost all results in three papers published in the Journal of Computational and Applied Mathematics, Applied Mathematics Letters, and Applied Mathematics and Computation in the years 2006, 2011, and 2014 by seven mathematicians. The proofs in the paper unify and are simpler than those in the three papers.
引用
收藏
页码：425 / 434
页数：10
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