On Some Properties and Inequalities for the Nielsen's $\beta$-Function

zbMath1429.33006arXiv1708.06604MaRDI QIDQ5205878

Kwara Nantomah

Publication date: 17 December 2019

Full work available at URL: https://arxiv.org/abs/1708.06604

zbMATH Keywords

inequalitydigamma functionsubadditivesuperadditiveNielsen's \(\beta \)-function

Mathematics Subject Classification ID

Gamma, beta and polygamma functions (33B15) Monotonic functions, generalizations (26A48)

Related Items (1)

Proof of a Conjecture on Nielsen

Cites Work

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• Conditions for convexity of a derivative and some applications to the gamma function
• The polygamma function \(\psi^{(k)}(x)\) for \(x={1\over 4}\) and \(x={3\over 4}\)
• Some infinite series involving the Riemann zeta function
• The integrals in Gradshteyn and Ryzhik. Part 11: The incomplete beta function
• The integrals in Gradshteyn and Ryzhik. Part 10: the digamma function

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