[en] In this work some new, preliminary formulae for slow neutron scattering cross section calculation by heavy and light water molecules have been done. The idea was to find, from the sum which exists in well known Nelkin model, other cross sections in a more simple analytical form, so that next approximations may be possible. In order to sum a series it was starting from Euler-Mclaurin formula. Some new summation formulae have been derived there, and defined in two theorems. Extensive calculations, especially during the evaluation of residues, have been made at the CDC 3600 computer. validation of derived formulae was done by comparison with the BNL-325 results. Good agreement is shown. (author)