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We compute systematically for the planar double box Feynman integral relevantto top pair production with a closed top loop the Laurent expansion in thedimensional regularisation parameter $\varepsilon$. This is done bytransforming the system of differential equations for this integral and all itssub-topologies to a form linear in $\varepsilon$, where the$\varepsilon^0$-part is strictly lower triangular. This system is easily solvedorder by order in the dimensional regularisation parameter $\varepsilon$. Thisis an example of an elliptic multi-scale integral involving several ellipticsub-topologies. Our methods are applicable to similar problems.

The planar double box integral for top pair production with a closed top loop to all orders in the dimensional regularisation parameter