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Some monotonicity properties of gamma and qgamma functions, Available onlie at http://arxiv.org/abs/0709.1126v2
"... Abstract. We prove some properties of completely monotonic functions and apply them to obtain results on gamma and qgamma functions. 1. ..."
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Abstract. We prove some properties of completely monotonic functions and apply them to obtain results on gamma and qgamma functions. 1.
MONOTONICITY AND CONCAVITY PROPERTIES OF SOME FUNCTIONS INVOLVING THE GAMMA FUNCTION WITH APPLICATIONS
"... ABSTRACT. In this article, we give the monotonicity and concavity properties of some functions involving the gamma function and some equivalence sequences to the sequence n! with exact equivalence constants. ..."
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ABSTRACT. In this article, we give the monotonicity and concavity properties of some functions involving the gamma function and some equivalence sequences to the sequence n! with exact equivalence constants.
A sharp inequality involving the psi function
 Acta Universitatis Apulensis
"... Abstract. The aim of this paper is to show that for a ∈ (0, 1) , the function fa (x) = ψ (x + a) − ψ (x) − a/x is strictly completely monotonic in (0, ∞). This result improves a previous result of Qiu and Vuorinen [Math. Comp. 74(2004) 723742], who proved that f 1/2 is strictly decreasing and co ..."
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Abstract. The aim of this paper is to show that for a ∈ (0, 1) , the function fa (x) = ψ (x + a) − ψ (x) − a/x is strictly completely monotonic in (0, ∞). This result improves a previous result of Qiu and Vuorinen [Math. Comp. 74(2004) 723742], who proved that f 1/2 is strictly decreasing and convex in (0, ∞). As a direct consequence, a sharp inequality involving the psi function is established. 2000 Mathematics Subject Classification: 33B15, 05A16 1. Introduction and
AN ELEMENTARY INEQUALITY FOR PSI FUNCTION BY
"... For x> 0, let Γ(x) be the Euler’s gamma function, and be the psi function. In this paper, we prove that (b−L(a,b))Ψ(b)+(L(a,b)−a)Ψ(a)> (b−a)Ψ ( √ ab) for b> a ≥ 2, where L(a, b) = b−a log b−log a. 1. ..."
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For x> 0, let Γ(x) be the Euler’s gamma function, and be the psi function. In this paper, we prove that (b−L(a,b))Ψ(b)+(L(a,b)−a)Ψ(a)> (b−a)Ψ ( √ ab) for b> a ≥ 2, where L(a, b) = b−a log b−log a. 1.