  We investigate the relation between the Riesz and the B{\'a}ez-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 B{\'a}ez-Duarte formulation. It is shown that $R(x)$ can
be expressed by $c_k$, and, vice versa, the sequence $c_k$ can be obtained from
the values of $R(x)$ at integer arguments. Also, we give some relations
involving $c_k$ and $R(x)$, and value of the alternating sum of $c_k$.
