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

Abstract

© 2017 Elsevier Inc. 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.