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Module « scipy.special »

Fonction gammaln - module scipy.special

Signature de la fonction gammaln

def gammaln(*args, **kwargs) 

Description

help(scipy.special.gammaln)

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


    gammaln(x, out=None)

    Logarithm of the absolute value of the gamma function.

    Defined as

    .. math::

       \ln(\lvert\Gamma(x)\rvert)

    where :math:`\Gamma` is the gamma function. For more details on
    the gamma function, see [dlmf]_.

    Parameters
    ----------
    x : array_like
        Real argument
    out : ndarray, optional
        Optional output array for the function results

    Returns
    -------
    scalar or ndarray
        Values of the log of the absolute value of gamma

    See Also
    --------
    gammasgn : sign of the gamma function
    loggamma : principal branch of the logarithm of the gamma function

    Notes
    -----
    It is the same function as the Python standard library function
    :func:`math.lgamma`.

    When used in conjunction with `gammasgn`, this function is useful
    for working in logspace on the real axis without having to deal
    with complex numbers via the relation ``exp(gammaln(x)) =
    gammasgn(x) * gamma(x)``.

    For complex-valued log-gamma, use `loggamma` instead of `gammaln`.

    References
    ----------
    .. [dlmf] NIST Digital Library of Mathematical Functions
              https://dlmf.nist.gov/5

    Examples
    --------
    >>> import numpy as np
    >>> import scipy.special as sc

    It has two positive zeros.

    >>> sc.gammaln([1, 2])
    array([0., 0.])

    It has poles at nonpositive integers.

    >>> sc.gammaln([0, -1, -2, -3, -4])
    array([inf, inf, inf, inf, inf])

    It asymptotically approaches ``x * log(x)`` (Stirling's formula).

    >>> x = np.array([1e10, 1e20, 1e40, 1e80])
    >>> sc.gammaln(x)
    array([2.20258509e+11, 4.50517019e+21, 9.11034037e+41, 1.83206807e+82])
    >>> x * np.log(x)
    array([2.30258509e+11, 4.60517019e+21, 9.21034037e+41, 1.84206807e+82])
    

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