`_arb_poly_sinh_cosh_series_basecase, arb_poly_sinh_cosh_series_basecase, _arb_poly_sinh_cosh_series_exponential, arb_poly_sinh_cosh_series_exponential, _arb_poly_sinh_cosh_series, arb_poly_sinh_cosh_series, _arb_poly_sinh_series, arb_poly_sinh_series, _arb_poly_cosh_series, arb_poly_cosh_series`

Synopsis#include <flint/arb_poly.h>

void _arb_poly_sinh_cosh_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)source

void arb_poly_sinh_cosh_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec)source

void _arb_poly_sinh_cosh_series_exponential(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)source

void arb_poly_sinh_cosh_series_exponential(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec)source

void _arb_poly_sinh_cosh_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)source

void arb_poly_sinh_cosh_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec)source

void _arb_poly_sinh_series(arb_ptr s, arb_srcptr h, slong hlen, slong n, slong prec)source

void arb_poly_sinh_series(arb_poly_t s, const arb_poly_t h, slong n, slong prec)source

void _arb_poly_cosh_series(arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)source

void arb_poly_cosh_series(arb_poly_t c, const arb_poly_t h, slong n, slong prec)source

Set s and/or c to $\sinh h$ and $\cosh h$ truncated to length n.

The basecase version uses the coupled recurrences that follow from $s' = h'c$ and $c' = h's$ , with $O(n \cdot \mathit{hlen})$ operations. The exponential version computes $e^h$ and $e^{-h}$ (one exponential and one inversion) and takes half their sum and difference. The default uses the basecase version for $\mathit{hlen}$ below 400 (for $\mathit{prec} \le 128$ ) or $30000 / (\ln \mathit{prec})^3$ .

Cite this page

The FLINT team, “_arb_poly_sinh_cosh_series_basecase, arb_poly_sinh_cosh_series_basecase, _arb_poly_sinh_cosh_series_exponential, arb_poly_sinh_cosh_series_exponential, _arb_poly_sinh_cosh_series, arb_poly_sinh_cosh_series, _arb_poly_sinh_series, arb_poly_sinh_series, _arb_poly_cosh_series, arb_poly_cosh_series (arb_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/arb_poly/_arb_poly_sinh_cosh_series_basecase.html (generated 2026-11-02).

@misc{flint-doc-arb-poly-arb-poly-sinh-cosh-series-basecase,
  author       = {{The FLINT team}},
  title        = {{\_arb\_poly\_sinh\_cosh\_series\_basecase, arb\_poly\_sinh\_cosh\_series\_basecase, \_arb\_poly\_sinh\_cosh\_series\_exponential, arb\_poly\_sinh\_cosh\_series\_exponential, \_arb\_poly\_sinh\_cosh\_series, arb\_poly\_sinh\_cosh\_series, \_arb\_poly\_sinh\_series, arb\_poly\_sinh\_series, \_arb\_poly\_cosh\_series, arb\_poly\_cosh\_series (arb\_poly.h)}},
  howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
  year         = {2026},
  url          = {https://flintlib.org/doc/arb_poly/_arb_poly_sinh_cosh_series_basecase.html},
  note         = {Generated 2026-11-02}
}

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