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Completely monotonic functions involving the gamma and  -gamma functions |
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| Authors: | Arcadii Z. Grinshpan Mourad E. H. Ismail |
| Affiliation: | Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700 ; Department of Mathematics, University of Central Florida, Orlando, Florida 32816 |
| Abstract: | 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  -gamma functions. |
| Keywords: | Gamma function $q$-gamma function completely monotonic functions inequalities. |
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