A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function. (30th December 2010) - Zhao, Tie-Hong; Chu, Yu-Ming
Abstract : We show that the functionG α, β ( x ) = e x Γ ( x + a ) / ( x + β ) x + β is strictly logarithmically completely monotonic on( 0, ∞ ) if and only if( α, β ) ∈ ( α, β ) : 0 < α ≤ β and[ G α, β ( x ) ] - 1 is strictly logarithmically completely monotonic on( 0, ∞ ) if and only if( α, β ) ∈ ( α, β ) : 0 < β ≤ α - 1 / 2 .