Logarithmically Complete Monotonicity Properties Relating to the Gamma Function
Joint Authors
Chu, Yu-Ming
Zhao, Tie-Hong
Wang, Hua
Source
Issue
Vol. 2011, Issue 2011 (31 Dec. 2011), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2011-07-21
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
We prove that the function fα,β(x)=Γβ(x+α)/xαΓ(βx) is strictly logarithmically completely monotonic on (0,∞) if (α,β)∈{( α,β):1/α≤β≤1, α≠1}∪{(α,β):0<β≤1,φ1(α,β)≥0,φ2(α,β)≥0} and [fα,β(x)]-1 is strictly logarithmically completely monotonic on (0,∞) if (α,β)∈{(α,β):0<α≤1/2,0<β≤1}∪{(α,β):1≤β≤1/α≤2,α≠1}∪{(α,β):1/2≤α<1,β≥1/(1-α)}, where φ1(α,β)=(α2+α-1)β2+(2α2-3α+1)β-α and φ2(α,β)=(α-1)β2+(2α2-5α+2)β-1.
American Psychological Association (APA)
Zhao, Tie-Hong& Chu, Yu-Ming& Wang, Hua. 2011. Logarithmically Complete Monotonicity Properties Relating to the Gamma Function. Abstract and Applied Analysis،Vol. 2011, no. 2011, pp.1-13.
https://search.emarefa.net/detail/BIM-506289
Modern Language Association (MLA)
Zhao, Tie-Hong…[et al.]. Logarithmically Complete Monotonicity Properties Relating to the Gamma Function. Abstract and Applied Analysis No. 2011 (2011), pp.1-13.
https://search.emarefa.net/detail/BIM-506289
American Medical Association (AMA)
Zhao, Tie-Hong& Chu, Yu-Ming& Wang, Hua. Logarithmically Complete Monotonicity Properties Relating to the Gamma Function. Abstract and Applied Analysis. 2011. Vol. 2011, no. 2011, pp.1-13.
https://search.emarefa.net/detail/BIM-506289
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-506289