|本期目录/Table of Contents|

[1]杜培培,王根娣.Gamma函数的单调性与凹凸性[J].浙江理工大学学报,2022,47-48(自科四):608-614.
　DU Peipei,WANG Gendi.Monotonicity and convexity properties for the gamma function[J].Journal of Zhejiang Sci-Tech University,2022,47-48(自科四):608-614.
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Gamma函数的单调性与凹凸性()
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浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第47-48卷
期数:
2022年自科第四期
页码:
608-614
栏目:
出版日期:
2022-09-30

文章信息/Info

Title:
Monotonicity and convexity properties for the gamma function
文章编号:
1673-3851 (2022) 07-0608-07
作者:
杜培培; 王根娣
浙江理工大学理学院，杭州 310018
Author(s):
DU Peipei;  WANG Gendi
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
gamma函数; 单调性; 几何凹凸性; 对数凹凸性; 不等式
分类号:
O174-6
文献标志码:
A
摘要:
设α∈R,β≥0,x∈(0, ∞)，f α,β,±1 (x)≡e x Γ (x+β)x x+β-α ±1，获得了函数 f α,β,+1 的几何凹凸性，从而推广了 f  0,0,+1 的相应已知结果；将函数 f α,β,±1 中的指数函数替换为双曲函数，通过研究其单调性与对数凹凸性，获得了关于gamma函数的一些不等式，从而改进了gamma函数相应的已知不等式。

参考文献/References:

［1］ Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables［M］. Journal of Applied Mechanics, 1965, 32(1):10th ed. New York: Dover, 1972:255-260.

［2］ Qi F, Chen C P. Monotonicity and convexity results for functions involving the gamma function［J］. International Journal of Applied Mathematics and Computer Science, 2004, 1: 27-36.

［3］ Anderson G D, Barnard R W, Richards K C, et al. Inequalities for zerobalanced hypergeometric functions［J］. Transactions of the American Mathematical Society, 1995, 347(5): 1713-1723.

［4］ Zhou N H, Niu D W. Monotonicity properties related to the ratio of two gamma functions［J］. Mediterranean Journal of Mathematics, 2021, 18(3): 104.

［5］ Yang Z H, Tian J F. Monotonicity, convexity, and complete monotonicity of two functions related to the gamma function［J］. Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 2019, 113(4): 3603-3617.

［6］ 裘松良, 蔡传宇. Gamma函数和Psi函数的单调性与凹凸性［J］. 浙江理工大学学报(自然科学版), 2018, 39(1): 108-112.

［7］ Chu Y M, Zhang X M, Zhang Z H. The geometric convexity of a function involving gamma function with applications［J］. Communications of the Korean Mathematical Society, 2010, 25(3): 373-383.

［8］ Zhang X M, Xu T Q, Situ L B. Geometric convexity of a function involving gamma function and applications to inequality theory［J］. Journal of Inequalities in Pure and Applied Mathematics, 2007, 8(1): 17.

［9］ Anderson G D, Vamanamurthy M K, Vuorinen M. Generalized convexity and inequalities［J］. Journal of Mathematical Analysis and Applications, 2007, 335(2): 1294-1308.

［10］ Qi F, Chen C P. A complete monotonicity property of the gamma function［J］. Journal of Mathematical Analysis and Applications, 2004, 296(2): 603-607.

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备注/Memo

备注/Memo:
收稿日期：2021-09-24
基金项目：国家自然科学基金项目(11771400)
作者简介：杜培培(1997-)，女，河南商丘人，硕士研究生，主要从事复分析方面的研究
通信作者：王根娣，E-mail：gendi.wang@zstu.edu.cn
更新日期/Last Update: 2022-09-06