scipy.special.zetac¶
-
scipy.special.
zetac
(x) = <ufunc 'zetac'>¶ Riemann zeta function minus 1.
This function is defined as
\[\zeta(x) = \sum_{k=2}^{\infty} 1 / k^x,\]where
x > 1
. Forx < 1
the analytic continuation is computed. For more information on the Riemann zeta function, see [dlmf].- Parameters
- xarray_like of float
Values at which to compute zeta(x) - 1 (must be real).
- Returns
- outarray_like
Values of zeta(x) - 1.
See also
References
- dlmf
NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/25
Examples
>>> from scipy.special import zetac, zeta
Some special values:
>>> zetac(2), np.pi**2/6 - 1 (0.64493406684822641, 0.6449340668482264)
>>> zetac(-1), -1.0/12 - 1 (-1.0833333333333333, -1.0833333333333333)
Compare
zetac(x)
tozeta(x) - 1
for large x:>>> zetac(60), zeta(60) - 1 (8.673617380119933e-19, 0.0)