Asymptotic formulĂ¦ in combinatory analysis

Proceedings of the London Mathematical Society, 2, XVI, 1917,
Records for 1 March 1917

A preliminary account of some of the contents of this paper^{1}
appeared in the Comptes Rendus of January 2nd, 1917. The
paper contains a full discussion and proof of the results there stated. The
asymptotic formula for $p(n)$, the number of unrestricted partitions of $n$,
of which only the first three terms were given, is completed; and it is
shewn that, by taking a number of terms of order $\sqrt{n}$, the exact
value of $p(n)$ can be obtained for all sufficiently large values of $n$.
Some account is also given of actual or possible applications of the method
used to other problems in Combinatory Analysis or the Analytic Theory of
Numbers.

Endnotes

^{1}[No. 36 of this volume.]