Completely monotonic functions involving the gamma and q-gamma functions

We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma f...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 2006-04, Vol.134 (4), p.1153-1160
Main Authors: Grinshpan, Arcadii Z., Mourad E. H. Ismail
Format: Article
Language:English
Subjects:
Exact sciences and technology
Gamma function
Income inequality
Mathematical analysis
Mathematical functions
Mathematical independent variables
Mathematical inequalities
Mathematical integrals
Mathematical theorems
Mathematics
Monotonic functions
Real functions
Sciences and techniques of general use
Special functions
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Summary:We give an infinite family of functions involving the gamma function whose logarithmic derivatives are completely monotonic. Each such function gives rise to an infinitely divisible probability distribution. Other similar results are also obtained for specific combinations of the gamma and q-gamma functions.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-05-08050-0