Complete monotonicity of a function involving the divided difference of psi functions

Authors

  • F. Qi
  • P. Cerone
  • S. S. Dragomir

Keywords:

necessary and sufficient condition, complete monotonicity, logarithmically complete monotonicity, divided difference, ratio of two gamma functions, inequality, psi function, polygamma function

Abstract

In the paper, necessary and sufficient conditions are presented for a function involving the divided difference of the psi function to be completely monotonic and for a function involving the ratio of two gamma functions to be logarithmically completely monotonic. From these, some double inequalities are derived for bounding polygamma functions, divided differences of polygamma functions and the ratio of two gamma functions. 10.1017/S0004972712001025

Published

2013-08-11

Issue

Vol. 88 No. 2 (2013)

Section

Articles
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