On a functional equation connected to Gauss quadrature rule - Koclęga-Kulpa, Barbara; Szostok, Tomasz (Annales Mathematicae Silesianae, 2008)
We consider the functional equation F(y)−F(x) = (y−x)[f(αx+βy)+f(βx+αy)] stemming from Gauss quadrature rule. In previous results equations of this type with rational only coefficients α and β were considered. In this paper we allow these numbers to be irrational. We find all solutions of this equation for functions acting on ℝ. However, some results are valid also on integral domains.