Integral representation for three-loop banana graph

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 sunset subgraphs. In this paper, we have developed similar three-loop banana $d = 2-2\varepsilon$ dimensions. answer generalized up to any given order the $\varepsilon$-expansion and calculated numerically both below above threshold. We also demonstrate how used compute more complex containing as subgraph.