  This paper generalizes Weyl realization to a class of Lie superalgebras
$\mathfrak{g}=\mathfrak{g}_0\oplus \mathfrak{g}_1$ satisfying
$[\mathfrak{g}_1,\mathfrak{g}_1]=\{0\}$. First, we give a novel proof of the
Weyl realization of a Lie algebra $\mathfrak{g}_0$ by deriving a functional
equation for the function that defines the realization. We show that this
equation has a unique solution given by the generating function for the
Bernoulli numbers. This method is then generalized to Lie superalgebras of the
above type.
