A completely monotonic function involving the gamma and trigamma functions

作者：Qi, Feng^*

来源：Kuwait Journal of Science, 2016, 43(3): 32-40.

• Completely monotonic function
• gamma function
• inequality
• logarithmically completely monotonic function
• trigamma function

In this paper the author provides necessary and sufficient conditions on a for the function
1/2ln(2 pi)-x+(x-1/2)ln x-ln Gamma(x)+1/12 psi'(x+a)
and its negative to be completely monotonic on(0,infinity),where a >= 0 is a real number, Gamma(x) is the classical gamma function, and psi(x)=Gamma'(x)/Gamma(x) is the digamma function. As applications, some known results and new inequalities are derived.

• 出版日期2016-7
• 单位河南理工大学; 内蒙古民族大学; 天津工业大学