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Module « scipy.special »

Fonction binom - module scipy.special

Signature de la fonction binom

def binom(*args, **kwargs) 

Description

help(scipy.special.binom)

binom(x1, x2, /, out=None, *, where=True, casting='same_kind', order='K', dtype=None, subok=True[, signature])


    binom(x, y, out=None)

    Binomial coefficient considered as a function of two real variables.

    For real arguments, the binomial coefficient is defined as

    .. math::

        \binom{x}{y} = \frac{\Gamma(x + 1)}{\Gamma(y + 1)\Gamma(x - y + 1)} =
            \frac{1}{(x + 1)\mathrm{B}(x - y + 1, y + 1)}

    Where :math:`\Gamma` is the Gamma function (`gamma`) and :math:`\mathrm{B}`
    is the Beta function (`beta`) [1]_.

    Parameters
    ----------
    x, y: array_like
       Real arguments to :math:`\binom{x}{y}`.
    out : ndarray, optional
        Optional output array for the function values

    Returns
    -------
    scalar or ndarray
        Value of binomial coefficient.

    See Also
    --------
    comb : The number of combinations of N things taken k at a time.

    Notes
    -----
    The Gamma function has poles at non-positive integers and tends to either
    positive or negative infinity depending on the direction on the real line
    from which a pole is approached. When considered as a function of two real
    variables, :math:`\binom{x}{y}` is thus undefined when `x` is a negative
    integer.  `binom` returns ``nan`` when ``x`` is a negative integer. This
    is the case even when ``x`` is a negative integer and ``y`` an integer,
    contrary to the usual convention for defining :math:`\binom{n}{k}` when it
    is considered as a function of two integer variables.

    References
    ----------
    .. [1] https://en.wikipedia.org/wiki/Binomial_coefficient

    Examples
    --------
    The following examples illustrate the ways in which `binom` differs from
    the function `comb`.

    >>> from scipy.special import binom, comb

    When ``exact=False`` and ``x`` and ``y`` are both positive, `comb` calls
    `binom` internally.

    >>> x, y = 3, 2
    >>> (binom(x, y), comb(x, y), comb(x, y, exact=True))
    (3.0, 3.0, 3)

    For larger values, `comb` with ``exact=True`` no longer agrees
    with `binom`.

    >>> x, y = 43, 23
    >>> (binom(x, y), comb(x, y), comb(x, y, exact=True))
    (960566918219.9999, 960566918219.9999, 960566918220)

    `binom` returns ``nan`` when ``x`` is a negative integer, but is otherwise
    defined for negative arguments. `comb` returns 0 whenever one of ``x`` or
    ``y`` is negative or ``x`` is less than ``y``.

    >>> x, y = -3, 2
    >>> (binom(x, y), comb(x, y))
    (nan, 0.0)

    >>> x, y = -3.1, 2.2
    >>> (binom(x, y), comb(x, y))
    (18.714147876804432, 0.0)

    >>> x, y = 2.2, 3.1
    >>> (binom(x, y), comb(x, y))
    (0.037399983365134115, 0.0)
    

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