2006Journal of the Australian Mathematical SocietyOpen access

Some completely monotonic functions involving the gamma and polygamma functions

Feng Qi, Bai‐Ni Guo, Chao-Ping Chen

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Abstract

Abstract The function [Γ(x + 1)]1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞). The function ψ″ (x + 2) + (1 + x2)/x2(1 + x)2 is strictly completely monotonic in (0, ∞).

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Abstract The function [Γ(x + 1)]1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞). The function ψ″ (x + 2) + (1 + x2)/x2(1 + x)2 is strictly completely monotonic in (0, ∞).

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Abstract The function [Γ(x + 1)]1/x(1 + 1/x)x/x is strictly logarithmically completely monotonic in (0, ∞). The function ψ″ (x + 2) + (1 + x2)/x2(1 + x)2 is strictly completely monotonic in (0, ∞).

Key concepts: Monotonic function, Mathematics, Function (biology), Gamma function, Pure mathematics, Combinatorics, Discrete mathematics, Mathematical analysis

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