Inequalities involving the multiple psi function

In this work, multiple gamma functions of order n have been considered. The logarithmic derivative of the multiple gamma function is known as the multiple psi function. Subadditive, superadditive, and convexity properties of higher-order derivatives of the multiple psi function are derived. Some related inequalities for these functions and their ratios are also obtained. (C) 2018 Academie des sciences. Published by Elsevier Masson SAS. All rights reserved.