doiSerbia

The additivity of polygamma functions

Guo Bai-Ni (Henan Polytechnic University, School of Mathematics and Informatics, Jiaozuo City, Henan Province, China)
Qi Feng (Inner Mongolia University for Nationalities, College of Mathematics, Tongliao City, Inner Mongolia Autonomous Region, China + Tianjin Polytechnic University, College of Science, Department of Mathematics, Tianjin City, China)
Luo Qiu-Ming (Chongqing Normal University, Department of Mathematics, Chongqing City, China)

In the paper, the authors prove that the functions |ψ(i)(ex)| for i  N are subadditive on (lnθi,∞) and superadditive on (-∞, ln θi), where θi  (0,1) is the unique root of equation 2|ψ(i)(θ)|= ψ(i)(θ2)|.

Keywords: subadditive function, super additive function, polygamma function