Mortici, Cristinel A sharp inequality involving the psi function. (English) Zbl 1212.33002 Acta Univ. Apulensis, Math. Inform. 21, 41-45 (2010). Summary: The aim of this paper is to show that for \(a\in (0,1)\), the function \(f_a(x)=\psi(x+a)-\psi(x)-a/x\) is strictly completely monotonic on \((0,\infty)\). This result improves a previous result of S.-L. Qiu and M. Vuorinen [Math. Comput. 74, No. 250, 723–742 (2005; Zbl 1060.33006)], who proved that \(f_{1/2}\) is strictly decreasing and convex on \((0,\infty)\). As a direct consequence, a sharp inequality involving the psi function is established. Cited in 2 Documents MSC: 33B15 Gamma, beta and polygamma functions 05A16 Asymptotic enumeration Keywords:gamma function; polygamma function; digamma function; psi function Citations:Zbl 1060.33006 PDFBibTeX XMLCite \textit{C. Mortici}, Acta Univ. Apulensis, Math. Inform. 21, 41--45 (2010; Zbl 1212.33002) Full Text: EuDML