FLINT3.7.0-dev
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_acb_poly_pow_acb_series, acb_poly_pow_acb_series

Synopsis#include <flint/acb_poly.h>
void _acb_poly_pow_acb_series(acb_ptr h, acb_srcptr f, slong flen, const acb_t g, slong len, slong prec)source
void acb_poly_pow_acb_series(acb_poly_t h, const acb_poly_t f, const acb_t g, slong len, slong prec)source

Set h to fg=exp⁡(glog⁡f)f^g = \exp(g \log f) for a constant exponent gg, truncated to length len. The underscore version requires positive lengths with flen≤len\mathit{flen} \le \mathit{len} and no aliasing.

Special cases: if gg is an exact real integer with ∣g∣<263|g| < 2^{63}, binary exponentiation is used (followed by an inversion if g<0g < 0); if f=a+bxdf = a + bx^d is a binomial, the coefficients come from the binomial series (_acb_poly_binomial_pow_acb_series); if g=±1/2g = \pm 1/2 exactly, _acb_poly_sqrt_series or _acb_poly_rsqrt_series is used; otherwise exp⁡(glog⁡f)\exp(g \log f).

Cite this page

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