For a positive integer n, the partition function, p(n), gives the number of ways of writing the integer n as a sum of positive integers, where the order of addends is not considered. p ( n ) ∼ 1 4 n 3 e π 2 n 3 {\displaystyle p(n)\sim {\frac {1}{4n{\sqrt {3}}}}e^{\pi {\sqrt {\frac {2n}{3}}}}}