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Anderson and Qiu (1997) conjectured that the function log Γ (x+1)x log x is concave for $x>1$. In this paper we prove this conjecture. We also study the monotonicity of some functions connected with the psi-function ψ (x) and derive inequalities for ψ (x) and ψ ’(x).
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Elbert et al. (2000) studied this question.
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