A Class of Logarithmically Completely Monotonic Functions Associated with a Gamma Function. (30th December 2010)

• Record Type: Journal Article
• Authors: Zhao, Tie-Hong; Chu, Yu-Ming
• Other Names: Ding Shusen Academic Editor.
• Is Part Of: Journal of inequalities and applications. Volume 2010(2010)
• Publication Date: 2010-12-30
• Subjects: Inequalities (Mathematics) -- Periodicals; 512.97
• DOI: 10.1155/2010/392431
• Languages: English
• ISSNs: 1029-242X

Abstract

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 } .