Factorials and gamma functions
------------------------------

.. contents::

Factorials (:func:`factorial`/:func:`fac`)
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.. autofunction:: mpmath.functions.factorial(x, **kwargs)

Gamma function (:func:`gamma`, :func:`gammaprod`, :func:`loggamma`)
...................................................................

.. autofunction:: mpmath.functions.gamma(x, **kwargs)
.. autofunction:: mpmath.functions.gammaprod(a, b)
.. autofunction:: mpmath.functions.loggamma(x)

Binomial coefficients, rising and falling factorials (:func:`binomial`, :func:`rf`, :func:`ff`)
...............................................................................................

.. autofunction:: mpmath.functions.binomial(n,k)
.. autofunction:: mpmath.functions.rf(x,n)
.. autofunction:: mpmath.functions.ff(x,n)

Beta function (:func:`beta`)
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.. autofunction:: mpmath.functions.beta(x,y)

Double factorials (:func:`fac2`)
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.. autofunction:: mpmath.functions.fac2(x)

Super- and hyperfactorials (:func:`superfac`, :func:`hyperfac`, :func:`barnesg`)
................................................................................

.. autofunction:: mpmath.functions.superfac(z)
.. autofunction:: mpmath.functions.hyperfac(z)
.. autofunction:: mpmath.functions.barnesg(z)

Polygamma functions (:func:`psi`, :func:`digamma`, :func:`trigamma`, :func:`harmonic`)
......................................................................................

.. autofunction:: mpmath.functions.psi(m, z)
.. autofunction:: mpmath.functions.digamma(z)
.. autofunction:: mpmath.functions.trigamma(z)
.. autofunction:: mpmath.functions.harmonic(z)
