Module « scipy.special »

Fonction zetac - module scipy.special

Signature de la fonction zetac

Description

zetac.__doc__

zetac(x, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature, extobj])

zetac(x)

Riemann zeta function minus 1.

This function is defined as

.. math:: \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
----------
x : array_like of float
    Values at which to compute zeta(x) - 1 (must be real).

Returns
-------
out : array_like
    Values of zeta(x) - 1.

See Also
--------
zeta

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)

References
----------
.. [dlmf] NIST Digital Library of Mathematical Functions
          https://dlmf.nist.gov/25