Gamma Functions
==========================================

The gamma function is a special function extending the factorial to real numbers.

.. funcsketch:function:: gamma(x)

    Gamma function.

    :param x: The value to take the gamma function of.
    :type x: Real
    :definition: :math:`\Gamma(x) = \displaystyle\int_0^\infty t^{x-1} e^{-t} \, dt` for :math:`x > 0`,
        extended to the rest of the domain by analytic continuation.
    :domain: :math:`x \in \mathbb{R}`, excluding :math:`0, -1, -2, \ldots`
    :range: :math:`(-\infty, \infty)`, excluding :math:`0`
    :returns: The value of :math:`\Gamma(x)`.
    :rtype: Real

.. funcsketch:function:: lgamma(x)

    Natural logarithm of the absolute value of the gamma function.

    :param x: The value to take the function of.
    :type x: Real
    :definition: :math:`\mathrm{lgamma}(x) = \log{|\Gamma(x)|}`
    :domain: :math:`x \in \mathbb{R}`, excluding :math:`0, -1, -2, \ldots`
    :range: :math:`(-\infty, \infty)`
    :returns: The value of :math:`\log{|\Gamma(x)|}`.
    :rtype: Real