  We investigate the relation between the Riesz and the Baez-Duarte criterion
for the Riemann Hypothesis. In particular we present the relation between the
function $R(x)$ appearing in the Riesz criterion and the sequence $c_k$
appearing in the Baez-Duarte formulation. It is shown that $R(x)$ can expressed
by $c_k$ and vice versa the sequence $c_k$ can be obtained from the values of
$R(x)$ at integer arguments. We give also some relations involving $c_k$ and
$R(x)$, in particular value of the alternating sum of $c_k$.
