Partition function (number theory): Difference between revisions

Revision as of 03:56, 24 March 2005

Revision as of 04:11, 24 March 2005

Line 73:

An [[asymptotic]] expression for ''p''(''n'') is given by

:<math>p(n) \sim \frac {\exp \pi \sqrt {2n/3}} {4n\sqrt{3}} \mbox { as } n\rightarrow \infty</math>

This expression was first optainedobtained by [[G. H. Hardy]] and [[Ramanujan]] in [[1918]] and independently by [[J. V. Uspensky]] in [[1920]].

In [[1937]], [[Hans Rademacher]] was able to improve on Hardy and Ramanjan's results by providing a convergent series expression for ''p''(''n''). It is