scipy.special.zetac — SciPy v1.15.2 Manual (original) (raw)

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:

scalar or ndarray

Values of zeta(x) - 1.

References

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)