Integral representations and complete monotonicity related to the remainder of Burnside's formula for the gamma function

被引：24

作者：

Qi, Feng ^{[1
]}

机构：

[1] Inner Mongolia Univ Nationalities, Coll Math, Tongliao City 028043, Inner Mongolia, Peoples R China

来源：

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS | 2014年 / 268卷

基金：

中国国家自然科学基金;

关键词：

Integral representation; Complete monotonicity; Logarithmically completely monotonic function; Remainder; Burnside's formula; Gamma function; APPROXIMATION; PROPERTY;

D O I：

10.1016/j.cam.2014.03.004

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the paper, the authors establish integral representations of some functions related to the remainder of Burnside's formula for the gamma function and find the (logarithmically) complete monotonicity of these and related functions. These results extend and generalize some known conclusions. (C) 2014 Elsevier B.V. All rights reserved.

引用

页码：155 / 167

页数：13

共 50 条

[21] COMPLETE MONOTONICITY OF THE REMAINDER OF AN ASYMPTOTIC EXPANSION OF THE GENERALIZED GURLAND'S RATIO
Yang, Zhen-Hang
Tian, Jing-Feng
MATHEMATICAL INEQUALITIES & APPLICATIONS, 2024, 27 (01): : 231 - 247
[22] Complete monotonicity of the remainder of the asymptotic series for the ratio of two gamma functions
Yang, Zhenhang
Tian, Jing-Feng
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2023, 517 (02)
[23] LOGARITHMICALLY COMPLETE MONOTONICITY PROPERTIES AND CHARACTERIZATIONS OF THE GAMMA FUNCTION
Li, Ai-Jun
Chen, Chao-Ping
TAMKANG JOURNAL OF MATHEMATICS, 2007, 38 (04): : 313 - 322
[24] INTEGRAL REPRESENTATIONS OF QUANTITIES ASSOCIATED WITH GAMMA FUNCTION
Kostin, A. B.
Sherstyukov, V. B.
UFA MATHEMATICAL JOURNAL, 2021, 13 (04): : 50 - 62
[25] Padé Approximant Related to Ramanujan’s Formula for the Gamma Function
Chao-Ping Chen
Results in Mathematics, 2018, 73
[26] Pad, Approximant Related to Ramanujan's Formula for the Gamma Function
Chen, Chao-Ping
RESULTS IN MATHEMATICS, 2018, 73 (03)
[27] Asymptotic expansions of the gamma function related to Windschitl's formula
Chen, Chao-Ping
APPLIED MATHEMATICS AND COMPUTATION, 2014, 245 : 174 - 180
[28] Some properties of extended remainder of binet's first formula for logarithm of gamma function
Qi, Feng
Guo, Bai-Ni
MATHEMATICA SLOVACA, 2010, 60 (04) : 461 - 470
[29] On complete monotonicity for several classes of functions related to ratios of gamma functions
Feng Qi
Ravi P. Agarwal
Journal of Inequalities and Applications, 2019
[30] Integral representations for the Gamma function, the Beta function, and the Double Gamma function
Choi, Junesang
Srivastava, H. M.
INTEGRAL TRANSFORMS AND SPECIAL FUNCTIONS, 2009, 20 (11) : 859 - 869

← 1 2 3 4 5 →