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We integrate three-loop sunrise-type vacuum diagrams in $D_0=4$ dimensionswith four different masses using configuration space techniques. The finiteparts of our results are in numerical agreement with corresponding three-loopcalculations in momentum space. Using some of the closed form results of themomentum space calculation we arrive at new integral identities involvingtruncated integrals of products of Bessel functions. For the non-degeneratefinite two-loop sunrise-type vacuum diagram in $D_0=2$ dimensions we make useof the known closed form $p$-space result to express the moment of a product ofthree Bessel functions in terms of a sum of Claussen polylogarithms. Usingresults for the nondegenerate two-loop sunrise diagram from the literature in$D_0=2$ dimensions we obtain a Bessel function integral identity in terms ofelliptic functions.

Coordinate space calculation of two- and three-loop sunrise-type diagrams, elliptic functions and truncated Bessel integral identities