Bounds and Completely Monotonicity of Some Functions Involving the Functions ψ′(l) and ψ″(l)

Symmetrical patterns exist in the nature of inequalities, which play a basic role theoretical and applied mathematics. In several studies, inequalities present accurate approximations functions based on their symmetry properties. paper, we prove completely monotonic (CM) property some involving function Δ(l)=ψ″(l)+ψ′(l)2 hence deduce new double inequality for it. Additionally, study CM degree ψ′(l). Our bounds takes priority over recently published results.