FLINT3.7.0-dev
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_fmpz_poly_eta_qexp, fmpz_poly_eta_qexp

Synopsis#include <flint/fmpz_poly.h>
void _fmpz_poly_eta_qexp(fmpz * f, slong e, slong n)source
void fmpz_poly_eta_qexp(fmpz_poly_t f, slong e, slong n)source

Set ff to the qq-expansion to length nn of (q−1/24η(q))e=∏k≥1(1−qk)e(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 ee. For e=−1e = -1 this is the generating function of the partition function, and for e=24e = 24, after multiplication by qq, the modular discriminant Δ\Delta, which generates the Ramanujan τ\tau function. Sparse formulas are used for e=1,2,3,4,6e = 1, 2, 3, 4, 6, and power series arithmetic reduces other ee 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 2026-11-02).