Approximation of the Partition Number After Hardy and Ramanujan: An Application of Data Fitting Method in Combinatorics

Abstract: Sometimes we need the approximate value of the partition number in a simple and efficient way. There are already several formulae to calculate the partition number p(n). But they are either inconvenient for most people (not majored in math) who do not want do write programs, or unsatisfying in accuracy. By bringing in two parameters in the Hardy-Ramanujan's Asymptotic formula and fitting the data of the two parameters by least square method, iteration method and some other special designed methods, several revised elementary estimation formulae with high accuracy for p(n) are obtained. With these estimation formulae, the approximate value of p(n) can be calculated by a pocket calculator without programming function. The main difficulty is that the usual methods to fit the data of the two parameters by an elementary function is defective here. These method could be used in finding the fitting functions of some other complex data.