_arb_poly_pow_arb_series, arb_poly_pow_arb_series
#include <flint/arb_poly.h>void _arb_poly_pow_arb_series(arb_ptr h, arb_srcptr f, slong flen, const arb_t g, slong len, slong prec)sourcevoid arb_poly_pow_arb_series(arb_poly_t h, const arb_poly_t f, const arb_t g, slong len, slong prec)sourceSet h to f^g = \exp(g \log f) for a constant exponent g, truncated to length len. The underscore version requires positive lengths with \mathit{flen} \le \mathit{len} and no aliasing.
Special cases: if g is an exact integer with |g| < 2^{63}, binary exponentiation is used (followed by an inversion if g < 0); if f = a + bx^d is a binomial, the coefficients come from the binomial series (_arb_poly_binomial_pow_arb_series); if g = \pm 1/2 exactly, _arb_poly_sqrt_series or _arb_poly_rsqrt_series is used; otherwise \exp(g \log f).
The FLINT team, “_arb_poly_pow_arb_series, arb_poly_pow_arb_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_pow_arb_series.html (generated 2026-10-20).
@misc{flint-doc-arb-poly-arb-poly-pow-arb-series,
author = {{The FLINT team}},
title = {{\_arb\_poly\_pow\_arb\_series, arb\_poly\_pow\_arb\_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_pow_arb_series.html},
note = {Generated 2026-10-20}
}