Completely monotonic functions involving the gamma and $q$-gamma functions
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- by Arcadii Z. Grinshpan and Mourad E. H. Ismail PDF
- Proc. Amer. Math. Soc. 134 (2006), 1153-1160 Request permission
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 $q$-gamma functions.References
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Additional Information
- Arcadii Z. Grinshpan
- Affiliation: Department of Mathematics, University of South Florida, Tampa, Florida 33620-5700
- Email: azg@math.usf.edu
- Mourad E. H. Ismail
- Affiliation: Department of Mathematics, University of Central Florida, Orlando, Florida 32816
- MR Author ID: 91855
- Email: ismail@math.ucf.edu
- Received by editor(s): April 12, 2004
- Received by editor(s) in revised form: October 28, 2004, and November 9, 2004
- Published electronically: September 28, 2005
- Additional Notes: The second author’s research was partially supported by NSF grant DMS 99-70865.
- Communicated by: Carmen C. Chicone
- © Copyright 2005 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 134 (2006), 1153-1160
- MSC (2000): Primary 33B15; Secondary 26A48
- DOI: https://doi.org/10.1090/S0002-9939-05-08050-0
- MathSciNet review: 2196051