Abstract and Applied Analysis

Research Article

Logarithmically Complete Monotonicity Properties Relating to the Gamma Function

Figure 2

The shading areas are respectively denoted by the subsets Ω 𝑖 for 𝑖 = 1 , 2 , … , 5 . The function 𝑓 𝛼 , 𝛽 ( 𝑥 ) is strictly logarithmically completely monotonic on ( 0 , ∞ ) if ( 𝛼 , 𝛽 ) ∈ Ω 1 ∪ Ω 2 , and [ 𝑓 𝛼 , 𝛽 ( 𝑥 ) ] − 1 is strictly logarithmically completely monotonic on ( 0 , ∞ ) if ( 𝛼 , 𝛽 ) ∈ Ω 3 ∪ Ω 4 ∪ Ω 5 .
896483.fig.002