partitions_rademacher_bound
Synopsis
#include <flint/partitions.h>Sets b to an upper bound for
M(n,N) = \frac{44 \pi^2}{225 \sqrt 3} N^{-1/2}
+ \frac{\pi \sqrt{2}}{75} \left( \frac{N}{n-1} \right)^{1/2}
\sinh\left(\frac{\pi}{N} \sqrt{\frac{2n}{3}}\right),
Rademacher's bound for the error of the Hardy–Ramanujan–Rademacher series truncated after the term k = N [Rademacher1937]. Requires n \ge 2 and N \ge 1. The constants are rounded upwards and the bound is evaluated with directed rounding at about 30 bits.
References#
- [Rademacher1937] Rademacher, Hans : On the partition function p(n) Proc. London Math. Soc vol. 43 (1937) 241–254
Cite this page
The FLINT team, “partitions_rademacher_bound (partitions.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/partitions/partitions_rademacher_bound.html (generated 2026-10-20).
@misc{flint-doc-partitions-partitions-rademacher-bound,
author = {{The FLINT team}},
title = {{partitions\_rademacher\_bound (partitions.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/partitions/partitions_rademacher_bound.html},
note = {Generated 2026-10-20}
}