Logarithmically complete monotonicity and Shur-convexity for some ratios of gamma functions
2006 ◽
pp. 88-92
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Define F(x) = ?(mx) xm-1?m(x) and G(x)- ?(mx) ?m(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 ?(x) = ? n i=1 ?(mxi + 1) ?m (x1 + 1) is strictly Schur-convex (-1/m,+?)n.
2013 ◽
Vol 219
(21)
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pp. 10538-10547
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2013 ◽
Vol 88
(2)
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pp. 309-319
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2017 ◽
Vol 2017
(1)
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2015 ◽
Vol 3
(3)
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pp. 130
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Keyword(s):
1978 ◽
Vol 23
(3)
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pp. 287-295
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