scipy.special.zetac#

scipy.special.zetac(x, out=None) = <ufunc 'zetac'>#

Riemann zeta function minus 1.

This function is defined as

\[\begin{split}\\zeta(x) = \\sum_{k=2}^{\\infty} 1 / k^x,\end{split}\]

where x > 1. For x < 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).
outndarray, optional: Optional output array for the function results

Returns:

See also

References

NIST Digital Library of Mathematical Functions https://dlmf.nist.gov/25

Examples

>>> import numpy as np
>>> 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) to zeta(x) - 1 for large x:

>>> zetac(60), zeta(60) - 1
(8.673617380119933e-19, 0.0)