|本期目录/Table of Contents|

[1]ZHAO Xue,QIU Song liang,CHEN Shi yong.Some Properties of Gamma, Beta and Psi Functions[J].浙江理工大学学报,2014,31-32(自科5):571-575.
　ZHAO Xue,QIU Song liang,CHEN Shi yong.Some Properties of Gamma, Beta and Psi Functions[J].Journal of Zhejiang Sci-Tech University,2014,31-32(自科5):571-575.
点击复制

Some Properties of Gamma, Beta and Psi Functions()
分享到：

浙江理工大学学报[ISSN:1673-3851/CN:33-1338/TS]

卷:
第31-32卷
期数:
2014年自科5期
页码:
571-575
栏目:
(自科)数学及应用
出版日期:
2014-09-10

文章信息/Info

Title:
Some Properties of Gamma, Beta and Psi Functions
文章编号:
1673-3851 (2014) 05-0571-05
作者:
ZHAO Xue;  QIU Song liang;  CHEN Shi yong
Author(s):
ZHAO Xue;  QIU Song liang;  CHEN Shi yong
School of Science, Zhejiang Sci-Tech University, Hangzhou 310018, China
关键词:
Gamma function;  Beta function;  Psi function;  monotonicity;  convexity;  inequality
分类号:
O156.4
文献标志码:
A
摘要:
This paper presents monotonicity and convexity properties of some combinations of Gamma function, Beta function and Psi function and gains progressive and accurate upper and lower bound of these important and special functions so as to improve and generalize several known results of these functions.

参考文献/References:

［1］ Abramowitz M, Stegun I A. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables［M］. New York, Dover, 1965: 253-294.
［2］ Qiu S L, Vuorinen M. Handbook of Complex Analysis: Special Function in Geometric Function Theory［M］. Elsevier B V, 2005: 621-659.
［3］ Anderson  G D, Vamanamurthy M K, Vuorinen M. Conformal Invariants, Inequalities, and Quasiconformal Mappings［M］. New York, John Wiley & Sons, 1997: 32-47.
［4］ Qiu S L, Vuorinen M. Some properties of the gamma and Psi functions with applications［J］. Mathematics of Computation, 2004, 74(250): 723-742.
［5］ Aderson G D, Qiu S L. A monotoneity property of the Gamma function［J］. Proc Amer Math Soc, 1997, 125(11): 3355-3362.
［6］ Alzer H. Gamma function inequalities［J］. Numer Algor, 2008, 49: 53-84.
［7］ Batir N. Inequalities for the gamma function［J］. Archiv der Mathematik, 2008, 91: 554-563.
［8］ Neuman E. Some inequalities for the gamma function［J］. Mathematics and Computation, 2011, 218(8): 4349-4352.
［9］ Qi F. Bounds for the Ratio of two gamma functions［J/OL］. J of Ineqs and Appls, 2010. ［2014-03-08］.http://downloads.hindawi.com/journals/jia/2010/493058.pdf.
［10］Elbert  , Laforgia A. On some properties of the gamma function［J］. The Amer Math Soc, 2000, 128(9): 2667-2673.
［11］Alzer  H. Inequalities for the gamma and polygamma functions［C］//Abhandlungen aus dem Mathematischen Seminar der Universitt Hamburg. Springer Berlin/Heidelberg, 1998, 68(1): 363-372.

相似文献/References:

[1]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,2018,39-40(自科1):108.
　QIU Songliang,CAI Chuanyu.Monotonicity and Convexity Properties of the Gamma and Psi Functions[J].Journal of Zhejiang Sci-Tech University,2018,39-40(自科5):108.

备注/Memo

备注/Memo:
Received Date：2014-03-08
Foundation item：This research is supported by the NSF of P. R. China (Grant No.114329A4A11652)
Introduction of the first author：ZHAO Xue(1988-), female, postgraduate student, Jinzhong Shanxi; Complex analysis
Corresponding author: QIU Song liang,E-mail:sl_qiu@zstu.edu.cn
更新日期/Last Update: 2014-09-26