A class of logarithmically completely monotonic functions related to the gamma function with applications

作者：Guo, Senlin; Qi, Feng; Srivastava, H. M.^*

来源：Integral Transforms and Special Functions, 2012, 23(8): 557-566.

DOI：10.1080/10652469.2011.611331

• necessary and sufficient condition
• logarithmically completely monotonic function
• inequalities
• gamma function
• psi (or digamma) function
• polygamma function
• zero-balanced hypergeometric F-p(p-1) series
• applications involving two-sided bounding inequalities

In this article, a necessary and sufficient condition and a necessary condition are established for a class of functions involving the gamma function to be logarithmically completely monotonic on (0,infinity). As applications of the necessary and sufficient condition, several two-sided bounding inequalities for the psi and polygamma functions and the ratio of two gamma functions are derived.

• 出版日期2012
• 单位河南理工大学; 中原工学院; 天津工业大学