Generating Functions for Pr1 (n) and Pr2 (n)

In 1970 George E. Andrews defined the generating functions for P r1 (n) and Pr2 (n) . In this article these generating functions are discussed elaborately. This paper shows how to prove the theorem P r2 (n)= P r3(n) with a numerical example when n = 9 and r = 2. In 1966 Andrews defined the terms A'(n) and B'(n), but this paper proves the remark A'(n)= B'(n) with the help of an example when n = 10. In 1961 N. Bourbaki defined the term P(n,m) . This paper shows how to prove a Remark in terms of P(n,m) , where P(n,m) is the number of partitions of the type of enumerated by P r3 (n) with the further restrictions that b1 <= 2m .

کلیدواژه ها:

Generating functions ، number of partitions