## Članak

 članak: 1 od 1
Publikacija Elektrotehničkog fakulteta - serija: matematika
2006, br. 17, str. 88-92
neklasifikovan
doi:10.2298/PETF0617088A

Logarithmically complete monotonicity and Shur-convexity for some ratios of gamma functions
(naslov ne postoji na srpskom)
aHenan Polytechnic University, School of Mathematics and Informatics, Jiaozuo City, Henan Province, China
bHenan Polytechnic University, School of Mathematics and Informatics, Research Institute of Applied Mathematics, Jiaozuo City, Henan, China

### Sažetak

(ne postoji na srpskom)
Define F(x) = Г(mx) xm-1Гm(x) and G(x)- Г(mx) Гm(x). for x > 0 and m = 2 3,…. In this paper, we consider the logarithmically complete monotonicity properties for the function F and 1/G, and we prove that the function φ(x) = ∏ n i=1 Г(mxi + 1) Гm (x1 + 1) is strictly Schur-convex (-1/m,+∞)n.

### Ključne reči

gamma function; psi function; (logarithmically) complete monotonic function; Schur-convex

### Reference

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