2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/187036Explicit formulas for the solutions of the recurrence relations for 3--loop vacuum integrals are suggested. This formulas can be used for direct calculations and demonstrate a high efficiency. They also produce a new type of recurrence relations over the space--time dimension.5 pages, misprint in the intermediate formula correctedHigh Energy Physics - PhenomenologyHigh Energy Physics - Theorytext