## NECESSARY AND SUFFICIENT CONDITIONS FOR A FUNCTION INVOLVING DIVIDED DIFFERENCES OF THE DI- AND TRI-GAMMA FUNCTIONS TO BE COMPLETELY MONOTONIC (903)

by
Feng Qi
,
Bai-ni Guo

Citations: | 7 - 7 self |

### BibTeX

@MISC{Qi903necessaryand,

author = {Feng Qi and Bai-ni Guo},

title = {NECESSARY AND SUFFICIENT CONDITIONS FOR A FUNCTION INVOLVING DIVIDED DIFFERENCES OF THE DI- AND TRI-GAMMA FUNCTIONS TO BE COMPLETELY MONOTONIC},

year = {903}

}

### OpenURL

### Abstract

Abstract. In the present paper, necessary and sufficient conditions are established for a function involving divided differences of the digamma and trigamma functions to be completely monotonic. Consequently, necessary and sufficient conditions are derived for a function involving the ratio of two gamma functions to be logarithmically completely monotonic, and some double inequalities are deduced for bounding divided differences of polygamma functions. 1.