In this paper we prove the Riemann hypothesis, that all zeros of the Riemann zeta function in the critical strip D := {z in C: 0 < Re z < 1} are simple and located on the critical line {z \in C: Re z = 1/2}. The main vehicle of our proof is the use of the special function} G(z) := Int_{0,\infty} y^{z-1}(1+\exp(y))^{-1} dy, which has the same zeros in the critical strip as the Riemann zeta function