`arith_bernoulli_number_size`

Synopsis#include <flint/arith.h>

double arith_bernoulli_number_size(ulong n)source

Returns $b$ such that $|B_n| < 2^{\lfloor b \rfloor}$ , from $|B_n| < 4 \cdot n!/(2\pi)^n$ and $n! \le (n+1)^{n+1} e^{-n}$ . Odd $n$ are not treated specially. The bound is evaluated in double precision and is not guaranteed for $n > 10^{14}$ .

Cite this page

The FLINT team, “arith_bernoulli_number_size (arith.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arith/arith_bernoulli_number_size.html (generated 2026-11-02).

@misc{flint-doc-arith-arith-bernoulli-number-size,
  author       = {{The FLINT team}},
  title        = {{arith\_bernoulli\_number\_size (arith.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arith/arith_bernoulli_number_size.html},
  note         = {Generated 2026-11-02}
}

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