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AI Summary & Key Takeaways
AI Insight⚡ TL;DR(Too Long; Didn't Read)
Stat. 39 (2), 219–231, 2010).
📌 3 Key Takeaways
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Objective & Hypothesis:Letbe the psi function, that is the logarithmic derivative of the Euler gamma function.
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Key Findings & Data:The aim of this paper is to establish an asymptotic formula for the function $psi(x)+log(e^{1/x}-1)$ and to improve some results of Batir (Some new inequalities for gamma and polygamma functions, J.
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Conclusion & Impact:Stat. 39 (2), 219–231, 2010).
🔬Design:Research Article
📍Scope:2005 Verileri
⚙️Variables:Domain Parameters
Abstract
Letbe the psi function, that is the logarithmic derivative of the Euler gamma function. The aim of this paper is to establish an asymptotic formula for the function $psi(x)+log(e^{1/x}-1)$ and to improve some results of Batir (Some new inequalities for gamma and polygamma functions, J. Ineq. Pure Appl. Math. 6 (4), Art 103, 2005) and Alzer (Sharp inequalities for the harmonic numbers, Expo. Math. 24, 385–388, 2006). Finally we give a short proof of, respectively, the monotonicity and concavity of the function $psi(x)+log(e^{1/x}-1)$ , previously stated by Alzer above, and by Guo and Qi (Some properties of the psi and polygamma functions, Hacet. J. Math. Stat. 39 (2), 219–231, 2010).
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Cite This Article
MORTİCİ, C. (2022). On a sum of the psi function with a logarithm. Hacettepe Journal of Mathematics and Statistics, Cilt: 40 - Sayı: 6, 775–780. https://ajindex.com/articles/530578