FLINT3.7.0-dev
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_arb_poly_atan_series, arb_poly_atan_series, _arb_poly_asin_series, arb_poly_asin_series, _arb_poly_acos_series, arb_poly_acos_series

Synopsis#include <flint/arb_poly.h>
void _arb_poly_atan_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)source
void arb_poly_atan_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)source
void _arb_poly_asin_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)source
void arb_poly_asin_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)source
void _arb_poly_acos_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)source
void arb_poly_acos_series(arb_poly_t res, const arb_poly_t f, slong n, slong prec)source

Set res to \operatorname{atan} f, \operatorname{asin} f or \operatorname{acos} f truncated to length n. The underscore versions allow aliasing. Wrappers of _gr_poly_atan_series, _gr_poly_asin_series and _gr_poly_acos_series.

The generic implementations integrate the derivative,

\operatorname{atan} f = \operatorname{atan} f_0 + \int \frac{f'}{1 + f^2}\, dx, \qquad \operatorname{asin} f = \operatorname{asin} f_0 + \int \frac{f'}{\sqrt{1 - f^2}}\, dx,

and \operatorname{acos} f = \operatorname{acos} f_0 - \int f' / \sqrt{1 - f^2}\, dx.

Cite this page

The FLINT team, “_arb_poly_atan_series, arb_poly_atan_series, _arb_poly_asin_series, arb_poly_asin_series, _arb_poly_acos_series, arb_poly_acos_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_atan_series.html (generated 2026-10-20).