Within the framework of the theory of irreducible tensor operators, using well -known general analytical results for double sums of products of two 3j-Wigner symbols, analytical expressions for single j m sums m for the valuesj1 j2 1 andj 2 parameters of the upper row 3j Wigner symbol are specified.The expressions obtained supplement the well-known analytical results of the theory of angular momentum and are in demand in solving, in particular, such problems of atomic physics as the construction of a nonrelativistic quantum theory of single and double bremsstrahlung when a photon is scattered by an atom (atomic ion).