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Completely monotonic ratios of basic and ordinary gamma functions.
- Source :
-
Aequationes Mathematicae . Jun2021, Vol. 95 Issue 3, p569-588. 20p. - Publication Year :
- 2021
-
Abstract
- We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical q = 1 case. In the latter case we further provide simple new sufficient conditions leading to many new examples of logarithmically completely monotonic gamma ratios. Finally, we apply some of our results to study monotonicity of some gamma ratios and rational functions. [ABSTRACT FROM AUTHOR]
- Subjects :
- *GAMMA functions
*MONOTONIC functions
Subjects
Details
- Language :
- English
- ISSN :
- 00019054
- Volume :
- 95
- Issue :
- 3
- Database :
- Academic Search Index
- Journal :
- Aequationes Mathematicae
- Publication Type :
- Academic Journal
- Accession number :
- 150235354
- Full Text :
- https://doi.org/10.1007/s00010-020-00767-6