By analyzing the feature of the process for the recycled waste gas in furnace, let the volume of waste circulation be constant, the guantitative mathematical relations between the volume flow of waste gas and the recycled times of waste gas which goes into combustion-supporting air in furnace were built, and the quantitative mathematical relations between the density of oxygen in waste gas and the recycled times were built. By using the limit mathematic law, the quantitative mathematical formulation of the limit density of oxygen was gotten. On the basis of this, the quantitative mathematical formulations of oxygen density in combustion-supporting air and in flammable mixture were built. By using the similar methods, the mathematical calculating formulations of the density for other compositions were inferred. It provides the base for checking and analyzing the gas composition at different stages in real production process.