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

Notes

Array API Standard Support

zetac has experimental support for Python Array API Standard compatible backends in addition to NumPy. Please consider testing these features by setting an environment variable SCIPY_ARRAY_API=1 and providing CuPy, PyTorch, JAX, or Dask arrays as array arguments. The following combinations of backend and device (or other capability) are supported.

Library	CPU	GPU
NumPy	✅	n/a
CuPy	n/a	✅
PyTorch	✅	⛔
JAX	⚠️ no JIT	⛔
Dask	✅	n/a

See Support for the array API standard for more information.

References

[dlmf]

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)