acb_hypgeom_chebyshev_t, acb_hypgeom_chebyshev_u
Synopsis
#include <flint/acb_hypgeom.h>Sets res to the Chebyshev polynomial or Chebyshev function of the first or second kind
T_n(z) = {}_2F_1\left(-n,n,\frac{1}{2},\frac{1-z}{2}\right), \qquad
U_n(z) = (n+1)\, {}_2F_1\left(-n,n+2,\frac{3}{2},\frac{1-z}{2}\right).
For word-size integer n the functions call acb_chebyshev_t_ui and acb_chebyshev_u_ui. Otherwise the hypergeometric series is used near z = 1, and the trigonometric representations T_n(\cos \theta) = \cos(n\theta) and U_n(\cos\theta) = \sin((n+1)\theta)/\sin\theta elsewhere.
Cite this page
The FLINT team, “acb_hypgeom_chebyshev_t, acb_hypgeom_chebyshev_u (acb_hypgeom.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_chebyshev_t.html (generated 2026-10-20).
@misc{flint-doc-acb-hypgeom-acb-hypgeom-chebyshev-t,
author = {{The FLINT team}},
title = {{acb\_hypgeom\_chebyshev\_t, acb\_hypgeom\_chebyshev\_u (acb\_hypgeom.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/acb_hypgeom/acb_hypgeom_chebyshev_t.html},
note = {Generated 2026-10-20}
}