Monotonicity of some functions involving the gamma and PSI functions
Date
2008Source
Mathematics of ComputationVolume
77Issue
264Pages
2261-2275Google Scholar check
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Let L(x): = x - Γ(x+t)/Γ(x+s) xs-t+1, where Γ(x) is Euler's gamma function. We determine conditions for the numbers s, t so that the function Ψ(x): = - Γ(x-s)/Γ(x+t) x t-s-1 L″(x) is strongly completely monotonie on (0, ∞). Through this result we obtain some inequalities involving the ratio of gamma functions and provide some applications in the context of trigonometric sum estimation. We also give several other examples of strongly completely monotonic functions defined in terms of T and ψ:= Γ′/Γ functions. Some limiting and particular cases are also considered. © 2008 American Mathematical Society.
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