A harmonic mean inequality for the digamma function and related results

@article{Alzer2017AHM,
  title={A harmonic mean inequality for the digamma function and related results},
  author={H. Alzer and G. J. O. Jameson},
  journal={Rendiconti del Seminario Matematico della Universit{\`a} di Padova},
  year={2017},
  volume={137},
  pages={203-209}
}
  • H. Alzer, G. J. O. Jameson
  • Published 2017
  • Mathematics
  • Rendiconti del Seminario Matematico della Università di Padova
  • We present some inequalities and a concavity property of the digamma function ψ = Γ′/Γ, where Γ denotes Euler’s gamma function. In particular, we offer a new characterization of Euler’s constant γ = 0.57721.... We prove that −γ is the minimum of the harmonic mean of ψ(x) and ψ(1/x) for x > 0. Mathematics Subject Classification (2010). 33B15, 39B62, 41A44. 

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