_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
#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)sourcevoid arb_poly_sinh_cosh_series_basecase(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec)sourcevoid _arb_poly_sinh_cosh_series_exponential(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)sourcevoid arb_poly_sinh_cosh_series_exponential(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec)sourcevoid _arb_poly_sinh_cosh_series(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen, slong n, slong prec)sourcevoid arb_poly_sinh_cosh_series(arb_poly_t s, arb_poly_t c, const arb_poly_t h, slong n, slong prec)sourcevoid arb_poly_sinh_series(arb_poly_t s, const arb_poly_t h, slong n, slong prec)sourcevoid arb_poly_cosh_series(arb_poly_t c, const arb_poly_t h, slong n, slong prec)sourceSet 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.
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 2026-10-20).
@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 2026-10-20}
}