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General formalism of special form of Hylleraas correlated wave functions (SFHCWF) is demonstrated in this paper. The adequacy of the SFHCWF in the description as well as of the singlet than of the triplet excited states of two electron systems is also presented in this work. Application of SFHCWF to the calculations of doubly excited nl nl ′ states (n = 2-4) in the helium-like ions is done, using the screening constant by unit nuclear charge method in the framework of a variational procedure.doi:10.4208/jams.062910.072810a fatcat:qbu2pknownerde6jzqyimx5uey