The use of the so(2,l) algebra for the study of the two-electron atoms is suggested. The radial part of the two-electron function is expanded into the products of the one-electron functions. These one-electron functions form complete, entirely discrete set and are identified as the eigenfunctions of one of the generators of the so(2,l) algebra. By applying this algebra we are able to express all the matrix elements in analytic and numerically stable form. For matrix elements of the two-electron interaction this is done in three steps, all of them completely novel from the methodological point of view. First, repulsion integrals over four radial functions are written as a linear combination of the integrals over two radial functions and the coefficients of the linear combination are given in terms of hypergeometric functions. Second, combining algebraic technique with the integration by parts we derive recurrence relations for the repulsion integrals over two radial functions. Third, the derived recurrence relations are solved analytically in terms of the hypergeometric functions. Thus we succeed in expressing the repulsion integrals as rational functions of the hypergeometric functions. In this way we resolve the problem of the numerical stability of calculation of the repulsion integrals.
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