2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/224197In this article, we present analytical expansion results of two single mass scale four-loop vacuum integrals in d=3-2*ep dimensions. After finding hypergeometric representations with half-integer coefficients, we use algorithms which we implemented in FORM to expand these in terms of nested sums.4 pages, to appear in the Proceedings of SEWM08, Amsterdam, the Netherlands, August 26-29, 2008High Energy Physics - PhenomenologyMultiloop Bubbles for hot QCDtext