Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
9662493 | Computers & Mathematics with Applications | 2005 | 18 Pages |
Abstract
We consider the ratio T(x, y) = г(x)г(y) / г2((x + y)/2) and its properties related to convexity, logarithmic convexity, Schur-convexity, and complete monotonicity. Several new bounds and asymptotic expansions for T are derived. Sharp bounds for the function x â x/(1 - eâx) are presented, as well as bounds for the trigamma function. The results are applied to a problem related to the volume of the unit ball in Rn and also to the problem of finding the inverse of the function x â T(1/x, 3/x), which is of importance in applied statistics.
Related Topics
Physical Sciences and Engineering
Computer Science
Computer Science (General)
Authors
M. Merkle,