TWO MONOTONIC FUNCTIONS DEFINED BY TWO DERIVATIVES OF A FUNCTION INVOLVING TRIGAMMA FUNCTION

In the paper, by virtue of the convolution theorem for the Laplace transforms, with the help of monotonicity and logarithmic concavity of a function involving exponential function, and by means of analytic techniques, the author presents necessary and sufficient conditions for two functions defined by two derivatives of a function involving trigamma function to be completely monotonic or monotonic.

Automated summary

In this paper, the author investigates the complete monotonicity or monotonicity of two functions defined by the derivatives of a function involving the trigamma function. The conditions for these functions to be completely monotonic or monotonic are obtained using the convolution theorem for Laplace transforms, the monotonicity and logarithmic concavity of a function involving exponential function, and analytic techniques.