Complete monotonicity of divided differences of the di- and tri-gamma functions with applications

Feng Qi, Bai-Ni Guo
2016 Georgian Mathematical Journal  
AbstractIn the paper, we establish necessary and sufficient conditions for two families of functions involving divided differences of the di- and tri-gamma functions to be completely monotonic. Consequently, we derive necessary and sufficient conditions for two families of functions involving the ratio of two gamma functions to be logarithmically completely monotonic. Furthermore, we deduce some inequalities for bounding the ratio of two gamma functions and divided differences of polygamma functions.
more » ... s of polygamma functions.
doi:10.1515/gmj-2016-0004 fatcat:rjz7jxaxfjcslco765idgzwiye