scipy.special.zetac

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

Riemann zeta function minus 1.

This function is defined as

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

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

scalar or ndarray

Values of zeta(x) - 1.

See also

zeta

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) to zeta(x) - 1 for large x:

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