Gamma, digamma, polygamma functions - and an inequality of J.S. Martins
We give a survey talk on some recently published mean value inequalities for the classical gamma function, the digamma function and the polygamma functions. Further, we provide inequalities for the arithmetic, geometric, and harmonic means of the first n positive integers. These mean values can be expressed in terms of the gamma and digamma functions. Finally, we present an open problem concerning a converse of a mean value inequality of J.S. Martins, published in 1988.
May 18, 2001