An Inequality for the Psi Functions
نویسندگان
چکیده
For x > 0, let Γ(x) be the Euler's gamma function, and ψ(x) = Γ (x)/Γ(x) the psi function. In this paper, we prove that |ψ (n) (b) − ψ (n) (a)| < (b − L(a, b))|ψ (n+1) (b)| + (L(a, b) − a)|ψ (n+1) (a)| for all b > a > 0 and n = 0, 1, 2, · · ·, where L(a, b) = (b − a)/(log b − log a).
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