Recurrent relations combine the properties of arithmetic and geometric progressions, which accounts for their unique approximation abilities. This was illustrated by approximating the number of isomers of alkanes, the boiling points of homologs (nonlinear dependencies), the melting points of homologs (alternation effects), the temperature dependence of the solubility of inorganic salts in water, and by revealing the anomalies of gas chromatographic retention indices and retention times in reversed-phase high performance liquid chromatography.
The unique potential and different areas of applications of recurrent (synonymous: recursive) relationships in chemistry and chromatography are considered. Recurrent relations can be used in two forms: as functions of integer arguments, y(x + 1) = ay(x) + b, and as functions of equidistant argument values, A(x + ï„x) = aA(x) + b, ï„x = const. The first form is applicable to all physicochemical properties of homologs in organic chemistry, because the number of carbon (and other) atoms in a molecule can be integer only. The second one applies to chemical variables depending on temperature, pressure, concentrations, etc., when the chemists should provide equal “steps†of their variations.