`arith_euler_polynomial`

Synopsis#include <flint/arith.h>

void arith_euler_polynomial(fmpq_poly_t poly, ulong n)source

Sets poly to the Euler polynomial $E_n(x)$ , using

E_n(x) = \frac{2}{n+1}\left(B_{n+1}(x) - 2^{n+1}B_{n+1}\left(\frac{x}{2}\right)\right)

with $B_{n+1}(x)$ computed once by arith_bernoulli_polynomial and rescaled.

Cite this page

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

@misc{flint-doc-arith-arith-euler-polynomial,
  author       = {{The FLINT team}},
  title        = {{arith\_euler\_polynomial (arith.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arith/arith_euler_polynomial.html},
  note         = {Generated 2026-11-02}
}

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