ray, optional
        Optional output array for the function values

    Returns
    -------
    scalar or ndarray
        Value of the regularized incomplete beta function

    See Also
    --------
    beta : beta function
    betaincinv : inverse of the regularized incomplete beta function
    betaincc : complement of the regularized incomplete beta function
    scipy.stats.beta : beta distribution

    Notes
    -----
    The term *regularized* in the name of this function refers to the
    scaling of the function by the gamma function terms shown in the
    formula.  When not qualified as *regularized*, the name *incomplete
    beta function* often refers to just the integral expression,
    without the gamma terms.  One can use the function `beta` from
    `scipy.special` to get this "nonregularized" incomplete beta
    function by multiplying the result of ``betainc(a, b, x)`` by
    ``beta(a, b)``.

    This function wraps the ``ibeta`` routine from the
    Boost Math C++ library [2]_.

    References
    ----------
    .. [1] NIST Digital Library of Mathematical Functions
           https://dlmf.nist.gov/8.17
    .. [2] The Boost Developers. "Boost C++ Libraries". https://www.boost.org/.

    Examples
    --------

    Let :math:`B(a, b)` be the `beta` function.

    >>> import scipy.special as sc

    The coefficient in terms of `gamma` is equal to
    :math:`1/B(a, b)`. Also, when :math:`x=1`
    the integral is equal to :math:`B(a, b)`.
    Therefore, :math:`I_{x=1}(a, b) = 1` for any :math:`a, b`.

    >>> sc.betainc(0.2, 3.5, 1.0)
    1.0

    It satisfies
    :math:`I_x(a, b) = x^a F(a, 1-b, a+1, x)/ (aB(a, b))`,
    where :math:`F` is the hypergeometric function `hyp2f1`:

    >>> a, b, x = 1.4, 3.1, 0.5
    >>> x**a * sc.hyp2f1(a, 1 - b, a + 1, x)/(a * sc.beta(a, b))
    0.8148904036225295
    >>> sc.betainc(a, b, x)
    0.8148904036225296

    This functions satisfies the relationship
    :math:`I_x(a, b) = 1 - I_{1-x}(b, a)`:

    >>> sc.betainc(2.2, 3.1, 0.4)
    0.49339638807619446
    >>> 1 - sc.betainc(3.1, 2.2, 1 - 0.4)
    0.49339638807619446

    Úbetaincca™