Explicit solutions of the 3-loop vacuum integral recurrence relations

Explicit formulas for the solutions of the recurrence relations for 3-loop vacuum integrals are suggested. These 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. The efficiency of this approach is demonstrated by calculations of previously unknown coefficients in Taylor expansion of QED photon vacuum polarization for small q2.