Gronau, D.; Matkowski, J. Another characterization of the gamma function. (English) Zbl 1027.33001 Publ. Math. Debr. 63, No. 1-2, 105-113 (2003). Summary: The function \(\frac{\log\Gamma(x)}{\log x}\) is characterized to be the only convex solution of the functional equation \[ f(x+1)=\frac{\log x}{\log(x+1) }(f(x)+1), \quad x\in(0,\infty). \] Some relations to the function \({\log\Gamma(x+1)}/{x^a }\), \(0<a \leq 1\) are shown. Cited in 1 ReviewCited in 4 Documents MSC: 33B15 Gamma, beta and polygamma functions 39A13 Difference equations, scaling (\(q\)-differences) Keywords:gamma function; Bohr-Mollerup theorem PDFBibTeX XMLCite \textit{D. Gronau} and \textit{J. Matkowski}, Publ. Math. Debr. 63, No. 1--2, 105--113 (2003; Zbl 1027.33001)