Inequalities and completely monotonic functions associated with the ratios of functions resulting from the gamma function

摘要

We prove that some functions associated with the products Pi(n)(k-1) 2k-1/2k, Pi(n)(k-1) 3k-2/3k-1, Pi(n)(k-1) 3k-2/3k and Qn Pi(n)(k-1) 3k-1/3k are completely monotonic. By using the results obtained, we derive some inequalities for the previous products. Our results improve some known inequalities. (C) 2015 Published by Elsevier Inc.