On the evaluation of some three-body variational integrals

Stable recursive relations are presented for the numerical computation of the integrals $$\int d{\bf r}_1 d{\bf r}_2 r_1^{l-1} r_2^{m-1} r_{12}^{n-1} \exp{\{-\alpha r_1 -\beta r_2 -\gamma r_{12}\}}$$ ($l$, $m$ and $n$ integer, $\alpha$, $\beta$ and $\gamma$ real) when the indices $l$, $m$ or $n$ are negative. Useful formulas are given for particular values of the parameters $\alpha$, $\beta$ and $\gamma$.