Module « scipy.special »

Fonction zeta - module scipy.special

Signature de la fonction zeta

def zeta(x, q=None, out=None) 

Description

zeta.__doc__

    Riemann or Hurwitz zeta function.

    Parameters
    ----------
    x : array_like of float
        Input data, must be real
    q : array_like of float, optional
        Input data, must be real.  Defaults to Riemann zeta.
    out : ndarray, optional
        Output array for the computed values.

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

    Notes
    -----
    The two-argument version is the Hurwitz zeta function

    .. math::

        \zeta(x, q) = \sum_{k=0}^{\infty} \frac{1}{(k + q)^x};

    see [dlmf]_ for details. The Riemann zeta function corresponds to
    the case when ``q = 1``.

    See Also
    --------
    zetac

    References
    ----------
    .. [dlmf] NIST, Digital Library of Mathematical Functions,
        https://dlmf.nist.gov/25.11#i

    Examples
    --------
    >>> from scipy.special import zeta, polygamma, factorial

    Some specific values:

    >>> zeta(2), np.pi**2/6
    (1.6449340668482266, 1.6449340668482264)

    >>> zeta(4), np.pi**4/90
    (1.0823232337111381, 1.082323233711138)

    Relation to the `polygamma` function:

    >>> m = 3
    >>> x = 1.25
    >>> polygamma(m, x)
    array(2.782144009188397)
    >>> (-1)**(m+1) * factorial(m) * zeta(m+1, x)
    2.7821440091883969