Decreasing and complete monotonicity of functions defined by derivatives of completely monotonic function involving trigamma function (Q6590341)

Polygamma functions are defined by logarithmic derivatives of the Euler gamma function.\NMany works in the literature are focused on the study and applications of polygamma functions and inequalities involving them. In this paper, the authors find the necessary and sufficient conditions for a function defined by three derivatives of a function involving a trigamma function to be completely monotonic.\NThese results also confirm some previous open questions posed by the third author in [Appl. Anal. Discrete Math. 15, No. 2, 378--392 (2021; Zbl 1499.33012)].