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The exact representation of a two-electron wave function near the origin is the Fock expansion, i.e., a double summation over powers of R and of lnR [where R≡(r12+r22)1/2] with coefficients dependent on the five remaining angular variables. Using a representation of hyperspherical harmonics, we present here the first numerical solution of the equations for the Fock coefficients. We present also a general procedure for matching a linear combination of Fock-series solutions onto a basis of adiabatic hyperspherical functions at a matching radius R0. This matching procedure ensures that the proper asymptotic boundary conditions are satisfied. Exploratory numerical results are presented for 1S wave functions of He and H- in which four Fock-series solutions are matched onto the lowest 1S adiabatic hyperspherical wave function at a matching radius near the first antinode in the adiabatic wave function.