_fmpz_poly_eta_qexp, fmpz_poly_eta_qexp
Synopsis
#include <flint/fmpz_poly.h>void fmpz_poly_eta_qexp(fmpz_poly_t f, slong e, slong n)sourceSet f to the q-expansion to length n of (q^{-1/24} \eta(q))^e = \prod_{k \ge 1} (1 - q^k)^e, the Dedekind eta function without its leading factor, raised to the power e. For e = -1 this is the generating function of the partition function, and for e = 24, after multiplication by q, the modular discriminant \Delta, which generates the Ramanujan \tau function. Sparse formulas are used for e = 1, 2, 3, 4, 6, and power series arithmetic reduces other e to those.
Cite this page
The FLINT team, “_fmpz_poly_eta_qexp, fmpz_poly_eta_qexp (fmpz_poly.h),” FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev, 2026. https://flintlib.org/doc/fmpz_poly/_fmpz_poly_eta_qexp.html (generated 2026-10-20).
@misc{flint-doc-fmpz-poly-fmpz-poly-eta-qexp,
author = {{The FLINT team}},
title = {{\_fmpz\_poly\_eta\_qexp, fmpz\_poly\_eta\_qexp (fmpz\_poly.h)}},
howpublished = {FLINT: Fast Library for Number Theory, documentation, version 3.7.0-dev},
year = {2026},
url = {https://flintlib.org/doc/fmpz_poly/_fmpz_poly_eta_qexp.html},
note = {Generated 2026-10-20}
}