标题： 涉及差商的二阶和三阶伽马函数的函数的完全单调性的必要充分条件 显示英文标题

标题： Necessary and sufficient conditions for a function involving divided differences of the di- and tri-gamma functions to be completely monotonic

摘要： 在本文中，建立了涉及digamma函数和trigamma函数的差商函数为完全单调函数的充要条件。 由此，得到了涉及两个gamma函数比值的函数为对数完全单调函数的充要条件，并推导出了一些双不等式，用于界定多gamma函数的差商。 显示英文摘要

摘要： 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.