Location of Repository

Wendel-Gautschi-Kershaw's Inequalities and Sufficient and Necessary Conditions that a Class of Functions Involving Ratio of Gamma Functions are Logarithmically Completely Monotonic

Abstract

In the article, sufficient and necessary conditions that a class of\ud functions involving ratio of Euler’s gamma functions and originating from\ud Wendel-Gautschi-Kershaw’s double inequalities are logarithmically completely\ud monotonic are presented. From this, Wendel-Gautschi-Kershaw’s double inequalities\ud are refined, extended and sharpened

Topics: 0101 Pure Mathematics, 0103 Numerical and Computational Mathematics, Research Group in Mathematical Inequalities and Applications (RGMIA), sufficient and necessary condition, logarithmically completely monotonic function, Gautschi's double inequality, Kershaw's double inequality, Wendel's double inequality, ratio of gamma functions, elementary function involving the exponential function, monotonicity, refinement, sharpening, extension
Publisher: School of Communications and Informatics, Faculty of Engineering and Science, Victoria University of Technology
Year: 2007
OAI identifier: oai:eprints.vu.edu.au:17529
Sorry, we are unable to provide the full text but you may find it at the following location(s):

Citations

1. (2006). A class of logarithmically completely monotonic functions and application to the best bounds in the second Gautschi-Kershaw’s inequality,
2. (2006). A class of logarithmically completely monotonic functions and the best bounds in the ﬁrst Kershaw’s double inequality,
3. A class of logarithmically completely monotonic functions and the best bounds in the second Kershaw’s double inequality, submitted to
4. (2004). A complete monotonicity property of the gamma function,
5. (2006). A completely monotonic function involving divided diﬀerence of psi function and an equivalent inequality involving sum,
6. (2006). A completely monotonic function involving divided diﬀerences of psi and polygamma functions and an application,
7. (2006). A property of logarithmically absolutely monotonic functions and logarithmically complete monotonicities of (1 + α/x)x+β, Integral Transforms Spec. Funct.
8. (2000). cari´ c, The best bounds in Gautschi’s inequality,
9. (2005). Certain logarithmically N-alternating monotonic functions involving gamma and q-gamma functions,
10. (2004). Complete monotonicities of functions involving the gamma and digamma functions,
11. (1993). Completely Monotonic and Related Functions,
12. (2006). Completely monotonic functions involving the gamma and q-gamma functions,
13. (2006). Four logarithmically completely monotonic functions involving gamma function and originating from problems of traﬃc ﬂow,
14. (1984). Further inequalities for the gamma function,
15. (2006). Generalizations of a theorem of I. Schur,
16. (2004). Integral representation of some functions related to the gamma function,
17. (2006). Logarithmically complete monotonicity and Schurconvexity for some ratios of gamma functions,
18. (2005). Logarithmically complete monotonicity properties for the gamma functions,
19. (2007). Logarithmically completely monotonic functions concerning gamma and digamma functions,
20. (2006). Logarithmically completely monotonic functions involving gamma and polygamma functions,
21. (2006). Logarithmically completely monotonic functions relating to the gamma function,
22. (2005). Logarithmically completely monotonic ratios of mean values and an application,
23. (2005). Monotonicity and convexity for the gamma function,
24. (2006). Monotonicity and logarithmic convexity for a class of elementary functions involving the exponential function,
25. (2002). Monotonicity results and inequalities for the gamma and incomplete gamma functions,
26. (1948). Note on the gamma function,
27. (2006). On a completely monotonic function, Sh` uxu´ e de Sh´ ıji` an yˇ u R` ensh´ ı (Mathematics in Practice and
28. (1986). On gamma function inequalities,
29. (1967). On inﬁnitely divisible matrices, kernels and functions,
30. (2006). Some completely monotonic functions involving the gamma and polygamma functions,
31. (1959). Some elementary inequalities relating to the gamma and incomplete gamma function,
32. (1983). Some extensions of W. Gautschi’s inequalities for the gamma function,
33. (2006). Some gamma function inequalities,
34. (1988). Some properties of a class of logarithmically completely monotonic functions,
35. (2006). The best bounds in Gautschi-Kershaw inequalities,
36. (2006). The best bounds in Kershaw’s inequality and two completely monotonic functions,
37. (2007). Three classes of logarithmically completely monotonic functions involving gamma and psi functions, Integral Transforms Spec.
38. (2006). Three-log-convexity for a class of elementary functions involving exponential function,
39. (2006). Two logarithmically completely monotonic functions connected with gamma function,

To submit an update or takedown request for this paper, please submit an Update/Correction/Removal Request.