With the aid of convolution theorem of the Laplace transforms, a monotonicity rule for the ratio of two Laplace transforms, Bernstein’s theorem for completely monotonic functions, and other analytic techniques, the author presents decreasing property of a ratio constituted via three derivatives of a sum involving trigamma function and discovers necessary and sufficient conditions for a function constituted via three derivatives of a function involving trigamma function to be completely monotonic.

中文翻译：

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由涉及 trigamma 函数的函数的三个导数构成的两个函数的递减性质和完全单调性

借助拉普拉斯变换的卷积定理、两个拉普拉斯变换比的单调性规则、完全单调函数的伯恩斯坦定理和其他分析技术，作者提出了由三个导数构成的比的递减性质，包括trigamma 函数，并发现由涉及 trigamma 函数的函数的三个导数构成的函数完全单调的充要条件。