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

被引：31

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

页码：425 / 434

页数：10

共 29 条

[1]

[Anonymous], 2004, RGMIA RES REP COLL

[2]

[Anonymous], 1941, PRINCETON MATH SERIE

[3]

[Anonymous], 2009, TAMSUI OXFORD J MATH

[4]

[Anonymous], 2004, Mediterr. J. Math, DOI DOI 10.1007/S00009-004-0022-6

[5]

[Anonymous], 2014, Analytic Number Theory, Approximation Theory, and Special Functions, DOI [DOI 10.1007/978-1-4939-0258-316, 10.1007/978-1-4939-0258-3_16, DOI 10.1007/978-1-4939-0258-3_16]

[6]

[Anonymous], 2012, STUDIES MATH, DOI [DOI 10.1515/9783110269338, 10.1515/9783110269338]

[7]

[Anonymous], 2014, Glob. J. Math. Anal, DOI DOI 10.14419/GJMA.V2I3.2919

[8] On the degree of the weighted geometric mean as a complete Bernstein function [J].

Guo B.-N. ;

Qi F. .

Afrika Matematika, 2015, 26 (7-8) :1253-1262

[9] A completely monotonic function involving the tri-gamma function and with degree one [J].

Guo, Bai-Ni ;

Qi, Feng .

APPLIED MATHEMATICS AND COMPUTATION, 2012, 218 (19) :9890-9897

[10]

Guo BN, 2010, U POLITEH BUCH SER A, V72, P21

← 1 2 3 →