Normal-ordered equivalent of the Weyl ordering of ${\widehat{q}}^j{\widehat{p}}^k$

The problem of quantizing a bivariate dynamical system can be reduced to evaluating the ordering of ${\widehat{q}}^j{\widehat{p}}^k$. Here, we consider the Weyl ordering of ${\widehat{q}}^j{\widehat{p}}^k$ that is then expressed in term of the annihilation $\widehat{a}$ and creation ${\widehat{a}}^{†}$ operator. The explicit formula for the normal-ordered equivalent (all ${\widehat{a}}^{†}$’s preceeding all $\widehat{a}$'s) of the resulting expression is then given, and some relations are discussed.