The Euler-Riemann zeta function in some series formulae and its values at odd integer points

The paper presents formulae for certain series involving the Riemann zeta function. These formulae are generalizations, in a natural way, of well known formulae, originating from Leonhard Euler. Formulae that existed only for initial values n=0,1 are now found for every natural n. Relevant connections with various known results are also pointed out.