The best bounds in Gautschi's inequality

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Three classes of logarithmically completely monotonic functions involving gamma and psi functions (2007, background): “In order to establish the best bounds in Kershaw’s inequality (1), among other things, the papers [3, 5, 13, 18] established the following monotonicity and convexity property of zs,t(x): The function zs,t(x) is either convex and decreasing for |t− s| < 1 or concave and increasing for |t− s| > 1.”
Inequalities for the gamma function (2008, background): “Recently numerous interesting inequalities for the gamma function have been proved by many mathematicians, we refer to [1, 2, 3, 4, 5, 6, 7, 8, 10, 11, 12, 17, 20, 22], and the references therein.”
The Best Bounds in Gautschi-Kershaw Inequalities (2006, unknown): “The function ν ( x ) in [ 4, Theorem 5 ] can be rewritten as Since ν ( x ) is completely monotonic, then by definition of completely monotonic function we have for all nonnegative integer k .”
Asymptotic formulae associated with the Wallis power function and digamma function (2013, background): “for x 0 and 0 < s t , but the better bounds was already proved in [7].”
On some properties of digamma and polygamma functions (2007, unknown): “(cid:2) The second Gautschi–Kershaw inequality for the (cid:2) -function states that where 0 s 1, see [15,18].”