  It has recently been shown that two-loop kite-type diagrams can be computed
analytically in terms of iterated integrals with algebraic kernels. This result
was obtained using a new integral representation for two-loop sunset subgraphs.
In this paper, we have developed a similar representation for a three-loop
banana integral in $d = 2-2\varepsilon$ dimensions. This answer can be
generalized up to any given order in the $\varepsilon$-expansion and can be
calculated numerically both below and above the threshold. We also demonstrate
how this result can be used to compute more complex three-loop integrals
containing the three-loop banana as a subgraph.
