Quantum chromodynamics with infinite number of vector mesons

It is supposed that families of vector mesons ρ, ψ, Υ contain an infinite number of resonances with gradually increasing widths. The asymptotic freedom requirement involves a relationship between the electronic width of a resonance and its mass derivative over the number. Using of this relationship it is shown that for the families of ψ and Υ mesons the moment from experimental function R(s)is egual to the sum of the moment from a bare quark loop and the edge term which arised from replacing of summation by integration. These equalities are fulfilled up to 1% for 60 moments in the ψ-meson family and up to 2% for 96 moments in the Υ-meson family. The electronic widths of the considered resonances and the ρ-meson mass are calculated