纺织高校基础科学学报2016，Vol.29Issue(3)：299-305,7.DOI:10.13338/j.issn.1006-8341.2016.03.005
Gamma函数的相关函数及其q化的完全单调性
Complete monotonicity properties of functions involving the Gamma function and their q-analogues
摘要
Abstract
A investigation to derive the complete monotonicities of functions involving the Gam-ma function and their q-analogues is presented.First of all,using the integral representations and the monotonicity theory,it is proved that the complete monotonicities of functions Fα(x)=ψ'(x)+α/x-1/(x+1),fα(x)=lnx-ψ(x)-α/x and f(x)=lnx-ψ(x)+1/x2 on(0,∞);Second,based on the properties of q-analogues,the complete monotonicities of q-analogues about these three functions are respectively discussed by the series expansion of functions,the monotonicity theory and induction,and two inequalities are obtained because of the property.关键词
完全单调性/Gamma函数/q化函数/充分条件Key words
complete monotonicity/Gamma function/q-analogue function/sufficient condition分类
数理科学引用本文复制引用
李晶晶,孙梅..Gamma函数的相关函数及其q化的完全单调性[J].纺织高校基础科学学报,2016,29(3):299-305,7.基金项目
陕西省自然科学基金资助项目(2010JM1017) （2010JM1017）
